CAIIB – ABM (ADVANSE BANK MANAGEMENT)
CAIIB-ABM-IMPORTANT FORMULA
Important Formula
------------------------
Some of these Formula may not be applicable for ABM, but I request all of you to go
through all of them to understand the concepts clear for both ABM and BFM.
1. Raw material Turnover Ratio = Cost of RM used / Average stock of R M
2. SIP Turnover = Cost of Goods manufactured / Average stock of SIP
3. Debt Collection period = No. days or months or Weeks in a year/Debt Turnover Ratio.
4. Average Payment Period = No. days or months or Weeks in a year/Creditors Turnover
Ratio.
5. Inventory Turnover Ratio = Cost of Goods Sold / Average Inventory.
6. Debtors Turnover Ratio = Net Credit Sales / Average Debtors.
7. Creditors Turnover Ratio = Net Credit Purchases / Average Credits.
8. Defensive Interval Ratio = Liquid Assets / Projected Daily Cash Requirement
9. Projected daily cash requirement = Projected operating cash expenses / 365.
10. Debt Equity Ratio = Long Term Debt / Equity.
11. Debt Equity Ratio = Total outside Liability / Tangible Net Worth.
12. Debt to Total Capital Ratio = Total Debts or Total Assets/(Permanent Capital + Current
Liabilities)
13. Interest Coverage Ratio = EBIT / Interest.
14. Dividend Coverage Ratio = N. P. after Interest & Tax / Preferential dividend
15. Gross Profit Margin = Gross Profit / Net Sales * 100
16. Net Profit Margin = Net Profit / Net Sales * 100
17. Cost of Goods Sold Ratio = Cost of Goods Sold / Net Sales * 100.
18. Operating Profit Ratio = Earnings Before Interest Tax / Net Sales * 100
19. Expenses Ratio or Operating Ratio = Expenses / Net Sales * 100
20. Net Profit Ratio = Net Profit After interest and Tax / Net Sales * 100
21. Operating Expenses Ratio = (Administrative + Selling expenses) / Net Sales * 100
22. Administrative Expenses Ratio =(Administrative Expenses / Net Sales ) * 100
23. Selling Expenses Ratio =(Selling Expenses / Net Sales ) * 100
24. Financial Expenses Ratio = ( Financial Expenses / Net Sales ) * 100
25. Return on Assets = Net Profit After Tax / Total Assets.
26. Total Assets = Net Fixed Assets + Net Working Capital.
27. Net Fixed Assets = Total Fixed Assets – Accumulated Depreciation.
28. Net Working Capital = ( CA –CL ) – ( Intangible Assets + Fictitious Assets + Idle Stock
+ Bad Debts )
29. Return on Capital Employed = Net Profit Before Interest and Tax / Average Capital
Employed.
30. Average Capital employed = Equity Capital + Long Term Funds provided by Owners &
Creditors at the beginning & at the end of the accounting period divided by two.
31. Return on Ordinary Share Holders Equity = (NPAT – Preferential Dividends) / Average
Ordinary Share Holders Equity or Net Worth.
32. Earnings Per Share = Net Profit After Taxes and Preferential dividends / Number of
Equity Share.
33. Dividend per Share = Net Profit After Taxes and distributable dividend / Number of
Equity Shares.
34. Dividend Pay Out Ratio = Dividend per Equity Share / Earnings per Equity Share.
35. Dividend Pay Out Ratio = Dividend paid to Equity Share holders / Net Profit available
for Equity Share Holders.
36. Price Earning Ratio = Market Price per equity Share / Earning per Share.
37. Total Asset Turnover = Cost of Goods Sold / Average Total Assets.
38. Fixed Asset Turnover = Cost of Goods Sold / Average Fixed Assets.
39. Capital Turnover = Cost of Goods Sold / Average Capital employed.
40. Current Asset Turnover = Cost of Goods Sold / Average Current Assets.
41. Working Capital Turnover = Cost of Goods Sold / Net Working Capital.
42. Return on Net Worth = ( Net Profit / Net Worth ) * 100
43. DSCR = Profit after Tax & Depreciation + Int. on T L & Differed Credit + Lease
Rentals if any divided by Repayment of Interest & Installments on T L & Differed Credits +
Lease Rentals if any.
44. Factory Cost = Prime cost + Production Overheads.
45. Cost of Goods Sold = Factory Cost + Selling, distribution & administrative overheads
46. Contribution = Sales – Marginal Costs.
47. Percentage of contribution to sales = ( Contribution / Sales ) * 100
48. Break Even Analysis = F / ( 1 – VC / S )
F = Fixed costs, VC = Total variable operating costs & S = Total sales revenue
49. Break Even Margin or Margin of Safety = Sales – Break Even Point / Sales.
50. Cash Break Even = F – N / P – R or F – N / 1 – ( VC / S )
51. BEP = Fixed Costs / Contribution per unit.
52. Sales volume requires = Fixed cost + Required profit / Contribution per unit.
53. BEP in Sales = ( Fixed Costs / Contribution per unit ) * Price per unit.
54. Contribution Sales Ratio = ( Contribution per unit / Sale price per unit ) * 100
55. Level of sales to result in target profit after Tax = (Target Profit) / (1 – Tax rate /
Contribution per unit)
56. Level of sales to result in target profit = (Fixed Cost + Target profit) * sales price per
unit Contribution per unit.
57. Net Present Value = - Co + C1 / (1 + r)
58. Future expected value of a present cash flow = Cash Flow ( 1 + r ) ^ t
59. Present value of a simple future cash flow = Cash Flow / (1 + r) ^ t
60. The Discount Factor = 1 / (1 + r) ^ t
61. Notation used internationally for PV of an annuity is PV ( A, r, n )
62. Notation used internationally for FV of an annuity is FV ( A, r, n )
63. The effective annual rate = ( 1 + r ) ^ t – 1 or (1 + (r / N) ) – 1 )
N = Number of times compounding in a year
64. PV of end of period Annuity = A { (1- (1 / (1+r) ^ n) / r
65. CR = CA : CL
66. Net Worth = CA - CL
67. DER = TL/TNW or debt/equity or TL/equity
68. Price Elasticity of Supply = (% change in quantity supplied/(% change in price)
69. PV = P / R * [(1+R)^T - 1]/(1+R)^T
70. PV = P / (1+R)^T
71. FV = P * (1 + R)^T
72. FV = P*(1-R)^T
73. FV = P / R * [(1+R)^T - 1]
74. FV = P / R * [(1+R)^T - 1] * (1+R)
75. EMI = P * R * [(1+R)^T/(1+R)^T-1)]
76. FV of annuity = A/r ×{(1+r)^n-1}
77. Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
A bond has been issued with a face value of Rs. 1000 at 8% Coupon for 3 years. The
required rate of return is 7%. What is the value of the bond?
Explanation :
Here,
FV = 1000
Coupon Rate (CR) = 0.08
t = 3 yr
R (YTM) = 0.07
Coupon = FV × CR = 80
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So, Value of bond = 1026.25
(Since Coupon rate > YTM, so Bond’s Value > FV)
.............................................
A bond has been issued with a face value of Rs. 20000 at 12% Coupon for 3 years. The
required rate of return is 10%. What is the value of the bond?
Explanation :
Here,
FV = 20000
Coupon Rate (CR) = 0.12
t = 3 yr
R (YTM) = 0.10
Coupon = FV × CR = 2400
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So, Value of bond = 20995
(Since Coupon rate > YTM, so FV < Bond’s Value)
.............................................
A bond has been issued with a face value of Rs. 1000 at 10% Coupon for 3 years. The
required rate of return is 8%. What is the value of the bond if the Coupon amount is payable
on half-yearly basis?
Explanation :
Here,
FV = 1000
CR = 10% half-yearly = 5% p.a.
Coupon = FV × CR = 50
R = 8% yearly = 4% p.a.
t = 3 years
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
= 1052
(Since Coupon rate > YTM, so FV < Bond’s Value)
.............................................
A 10%, 6-years bond, with face value of Rs. 1000 has been purchased by Mr. x for Rs. 900.
What is his yield till maturity?
Explanation :
Here,
FV = 1000
CR = 10%
R (YTM) =?
T = 6 years
Coupon = FV × CR = 100
Bond’s price = 900
Since FV > Bond’s Value, Coupon rate < YTM (based on above three observations)
So, we have to use trial and error method. We have to start with a value > 10 and find the
price until we get a value < 900.
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So,
If YTM = 11%, price =957.69 (> 900, so keep guessing)
If YTM = 12%, price = 917.78 (> 900, so keep guessing)
If YTM = 13%, price = 880.06 (< 900, so stop)
So, YTM must lie between 12 and 13.
So, using interpolation technique,
YTM
= 12 + (917.78 – 900) ÷ (917.78 – 880.06)
= 12 + 17.78 ÷ 37.72
= 12.47%
(Verification: Putting R = 12.47% in bond’s price formula leads to value of 899.80 which is
closest to 900, so YTM = 12.47% is the right answer).
.............................................
Ram purchased two bonds bond-1 & bond-2 with face value of Rs. 1000 each and Coupon
of 8% and maturity of 4 years & 6 years respectively. If YTM is increased by 1%, the %
change in prices of bond-1 & bond-2 would be ......
Explanation :
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
Bond 1:
If YTM is 9%, then bond’s price
= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4
= 967.64
Bond 2:
If YTM is 9%, then bond’s price
= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6
= 955.14
So, % change in price of bond 1
= (1000 – 967.04) ÷ 1000
= 0.03296
= 3.29%
& % change in price of bond 2
= (1000 – 955.14) ÷ 1000
= 0.04486
= 4.48%
.............................................
Monica purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4
years. If YTM is increased by 1%, the change in price of bond would be......
Explanation :
If YTM is 9%, then bond’s price
= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4
= 967.604
So, change in price of the bond
= 1000 - 967.64
= 32.96 decrease
(Since Coupon rate < YTM, so Bond’s Value < FV)
.............................................
Ashwini purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 6
years. If YTM is increased by 1%, the change in price of bond would be......
Explanation :
If YTM is 9%, then bond’s price
= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6
= 955.14
So, change in price of the bond
= 1000 - 955.14
= Rs. 44.86 decrease
(Since Coupon rate < YTM, so Bond’s Value < FV)
.............................................
Priya purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4
years. If YTM is reduced by 2%, the change in price of bond would be......
Explanation :
If YTM = 6%, bond’s price
= [80 × (1.06^4 – 1) ÷ 0.06 + 1000] ÷ 1.06^4
= 1069.30,
So, change in price of the bond
= 1069.30 - 1000
= Rs. 69.30
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
Kumar invested in 10%, 3-year bond of face value of Rs. 1000. The expected market rate is
12%. What is the duration of the bond?
Explanation :
Bond’s Duration = ΣPV×t ÷ ΣP
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
ΣP = {100 × (1.123 -1) ÷ 0.12 + 1000} ÷ 1.123
= 951.6
Here 1 ÷ 1.12 = 0.89286, so a^t = 0.711787
ΣPV × t = 100 × 8.33336 × [0.288213 ÷ 0.10714286 – 3 × 0.711787] + 3000 × 0.711787
= 833.336 × (2.689988 – 2.135361) + 2135.361
= 462.19 + 2135.36 = 2597.55
So, Duration of the Bond
= 2597.55 ÷ 951.6
= 2.73 years
.............................................
Gaurav invested in 12.5%, 5-year bond of face value of Rs. 100. The expected market rate
is 15%. What is the duration of the bond?
Explanation :
Bond’s Duration = ΣPV×T ÷ ΣP
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
ΣP = {12.5 × (1.155 -1) ÷ 0.15 + 100} ÷ 1.155
= 91.6196
Here a = 0.86956 and a^t = 0.497176
So, ΣPV × T = 12.5 × 6.66636 × {0.502824 ÷ 0.13044 – 2.4588} + 248.588
= 116.33046 + 248.588 = 364.92
So, Duration of the Bond
= 364.92 / 91.6196
= 3.98 years
.............................................
Albert purchased 8%, 3 years bond of Rs. 10 lac, with annual interest payment and face
value payable on maturity. The YTM is assumed@ 6%. Calculate the duration and modified
duration.
Explanation :
Bond’s Duration = ΣPV×T ÷ ΣP
ΣP = 1053421
Now, a = 0.943396 and a^t = 0.839619
So, ΣPV×T = 80000 × 16.666 × (0.160381÷0.056604 – 2.518857) + 2518857
= 419370.767 + 25188579
= 2938227.77
So, Duration of the Bond
= 2938227.77 / 1053421
= 2.79 years
& Modified Duration
= Mckauley Duration ÷ (1 + R)
= 2.79 ÷ 1.06
= 2.63
.............................................
Salim purchased 8%, 3 years bond of Rs. 10 lac, with annual interest payment and face
value payable on maturity. The YTM is assumed@ 6%. Calculate % change in the price of
the bond when the decrease in YTM is 100 basis points from 6% to 5% and the duration is
2.79 years and modified duration is 2.63 years.
Explanation :
Percentage change in price of bond
= -MD × Change in Price
= -2.63 × (6% - 5%)
= 2.63%,
That means a fall in YTM by 1% increases the price of the bond by 2.63%.
.............................................
A 12%, 4-year bond of Rs. 100 was purchased by x for Rs. 100. If the market interest rate
increased by 1%, what will the market price?
Explanation :
P = 100
CR = 12%
YTM = 12 + 1 = 13%
So, Price = 97.03
.............................................
Mitalee is to receive Rs. 60000 from bank at the end of 3 years, being the maturity value of
a term deposit. How much he is depositing now, if the interest rate is 10%?
Explanation :
PV
= FV ÷ (1+r)T
= 60000 ÷ 1.3331
= Rs. 45078
.............................................
The cash flow expected from a project is Rs. 700, Rs. 1000 and Rs. 1200 in the 1st, 2nd, &
3rd year. The discounting factor @ 10% roi is 1.10, 1.21 and 1.331. What is the total
present value of these cash flows?
Explanation :
NPV = Σ {C÷ (1+r)T} – 1
Total Present Value
= Σ {C÷ (1+r)T}
= (700 ÷ 1.1) + (1000 ÷ 1.21) + (1200 ÷ 1.331)
= Rs. 2364
.............................................
Priyanka made an investment of Rs. 18000 and he expects a return of Rs. 3000 p.a. For 12
years. What is the present value and net present value of the cash flow @ 10% discount
rate?
Explanation :
PV = 20441
NPV = PV – 18000
= Rs. 2441
.............................................
Current yield on an 8% Rs. 100 bond is 7.5%. The price of the bond is ......
Explanation :
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
(Here, t = 1
So, price
= (Coupon + Face Value) ÷ (1 + R)
= (8 + 100) ÷ 1.075 = 100.465)
But, since Coupon Interest = Current Yield × Current Market Price
So, Price = 8 ÷ 7.5% = 8000 ÷ 75 = 106.67
.............................................
A 6 year bond is selling at Rs. 9500 with face value of Rs. 10000. The annual Coupon
amount is 800. What is the yield to maturity?
Explanation :
Since Coupon rate = 8% and market price < Face Value, so YTM must be > CR
Let CR be 9%. So, bond’s price = 9551.41 > 9500
Let CR be 10%, so price = 9128.95 < 9500
So, YTM must lie between 9 & 10.
Using interpolation technique,
YTM = 9% + (10-9) % × (9551.41 – 9500) ÷ (9551.41 – 9128.95)
= 9+51.41/422.46
= 9.12%
.............................................
A 15 year bond is trading at Rs. 958 with face value of Rs. 1000. The Coupon rate is 8%.
What is the yield to maturity?
Explanation :
Since trading value < face value, YTM is > CR
At 7%, price = 1091.08 > 958
And at YTM = 9%, price = 919.39 < 958,
so YTM lies somewhere between 7 and 9.
= 7 + (9-7) × (1091.08 – 958) / (1091.08 – 919.39)
= 7 + 2 × 133.08 / 171.69
= 8.5%
.............................................
A 3 year bond with par value Rs. 1000 has Coupon rate 12%. If the required rate of return is
10% and interest is payable semi - annually, find the value of the bond.
Explanation :
Here, interest is calculated semi-annually,
so Coupon = 1000 × 12% ÷ 2 = 60,
YTM = 10%/2 = 0.05,
T = 3 × 2 = 6 years
So, price = 1050
.............................................
The yield on a 6-year bond is 12% while that of 4-year bond is 9%. What should be the
yield on a 2-year bond beginning from now?
Explanation :
(1+12%)^6 = (1+9%)^4 × (1+r)^2
R = 18%
.............................................
A bond is issued with a face value of 1000 that pays a Rs. 25 Coupon semi-annually. Find
its Coupon rate.
Explanation :
Coupon = Face Value × Coupon Rate
25 = 1000 × CR ÷ 2
So, CR = 5%
.............................................
A 2-year bond offers a yield of 6% and a 3-year bond offers a yield of 7.5%. Under the
expectation theory, what should be the yield on a 1-year bond in 2 years?
Explanation :
(1+7.5%)^3 = (1+6%)^2 × (1+r)^1
R = 10.56%
.............................................
Find the price of a zero-Coupon bond maturing in 5 years and has a par value of 1000 and a
required yield of 6%.
Explanation :
Using bond’s price formula, here Coupon = 0 and hence,
Zero-Coupon Bond’s price = Face Value ÷ (1 + R)T = 1000 ÷ 1.065
But, unless otherwise mentioned, the required yield of most zero-Coupon bonds is based on
a semi-annual Coupon payment.
So, Price
= 1000 ÷ 1.0310
= 744
.............................................
A bond with a par-value of Rs. 100 is purchased for 95.92 and it paid a Coupon rate of 5%.
Calculate its current yield.
Explanation :
Coupon = Face value × Coupon Rate
And annual interest paid = Market Price × Current Yield
5 = 95.92 × CY
CY = 0.0521 = 5.21%
.............................................
A zero-Coupon bond has a future value of Rs. 1000 and matures in 2 years and can be
currently purchased for Rs. 925. Calculate its current yield.
Explanation :
Here
1000 = 925 × (1 + r)^2
So,
r = 1.0398 – 1
= 0.0398
= 3.98%
.............................................
You are receiving Rs. 1000 every year for the next 5 years at the beginning of the period
and you invest each payment @ 5%. How much you would at the end of the 5-year period?
Explanation :
Apply FV formula to get the Answer = 5802
.............................................
An annuity consists of monthly repayments of Rs. 600 made over 20 years and if rate is
14% monthly. What is the future value of the annuity?
Explanation :
Apply FV formula to get the Answer
Here
R = 14% / 12 = 0.01166
T = 20 × 12 = 240
FV = 781146
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
The measures of money including Bank deposit with RBI, Demand deposiit with the
banking system, Term deposit of banking systerm, currency with public, and other deposits
with RBI are shown as M0,M1,M2,M3.
1. The liabilities such as current deposits, demand liabilities portion of saving bank, margins
held against letter of credit or bank guarantee, balances in overdue fixed deposits are
included initially, in ......
a. M0
b. M1
c. M2
d. M3
Ans-b
2. The demand deposit of banks are included in ......
a. M0,M1
b. M1,M2
c. M2,M3
d. M1,M2,M3
Ans - b
3. The term deposit of banks are included in ......
a. M0,M1
b. M1,M2
c. M2,M3
d. M1,M2,M3
Ans - c
4. Major portion of which of the following contains, interest free funds and is the most
liquid part of money supply:
a. M0
b. M1
c. M2
d. M3
Ans - a
.....................................................
While releasing the data relating to inflation increased by the Govt, it is observed that
1) The consumer price index based inflation increased to 11% and
2) Whole sale price index based inflation increased to 8%
3) The govt. claims that due to implementation of Banks Bi-partite Settlement, there is
increase in demand of goods and services leading to increase in consumer prices.
4) Further due to increased wages and salaries, there is increase in cost of inputs leading to
increase in whole-sale price index.
Answer the following questions, based on the above information.
1. The inflation caused by the the information given at point no.3 in the question, is not
called as ...... (i) Core inflation, (ii) Demand Pull inflation (iii) Cost-push inflation
a. Only (i) and (ii)
b. Only (i) and (iii)
c. Only (ii) and (iii)
d. (i), (ii) and (iii)
Ans - b
2. The inflation rate of 8%, represented by the whole sale price, is called:
a. Core inflation
b. Headline inflation
c. Demand Pull inflation
d. Cost-push inflation
Ans - b
3. The inflation rate 11% represented by the consumer price, is called:
a. Core inflation
b. Headline inflation
c. Demand Pull inflation
d. Cost-push inflation
Ans - a
4. The inflation caused by the information given at point no.4 in the question, is not called
as ...... (i) Core inflation, (ii) Demand Pull inflation (iii) Cost-push inflation
a. Only (i) and (ii)
b. Only (i) and (iii)
c. Only (ii) and (iii)
d. (i), (ii) and (iii)
Ans - a
.........................................
By using the monetary policy, RBI regulates the money supply, availability of money and
also cost of money i.e.rate of interest. For this purpose, RBI makes use of no. of tools that
include Repo Rate, Bank Rate, Reverse Repo Rate, MSF Rate, SLR, CRR, Market
Stabilization scheme.
Based on this information answer the following question:
1. Which of the following ensures the solvency of commercial banks ?
a. Statutory Liquidity Ratio
b. Market Stablization Scheme
c. Cash Reverse Ratio
d. Repo and Reverse repo transaction
Ans - a
2. Change in which of the following reduce the funds available with banks for lending
purpose ?
a. Repo rate
b. Bank rate
c. Cash reverse Ratio
d. All the above
Ans - c
3. The rate of discount which is used by RBI for rediscounting of commercial instruments
from banks is represented by ......
a. Repo rate
b. Bank rate
c. MSF rate
d. Reverse Repo rate
Ans - b
4. Which of the following is used in the process of neutralizing the effect generated by
foreign exchange flows in india ?
a. Statutory Liquidity Ratio
b. Market Stablization Scheme
c. Cash Reverse Ratio
d. Repo and Reverse repo transaction
Ans - b
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
You are receiving Rs. 10000 every year for the next 5 years (at the beginning of the period)
and you invest each payment @ 5%. How much you would have at the end of the 5-year
period?
Explanation :
Here,
P = 10000
R = 5% p.a.
T = 5 yrs
If invested at the beginning,
FV = P / R * [(1+R)^T - 1] * (1+R)
FV = 55256 × 1.05
= 58019
.............................................
If you wish an annuity to grow to Rs. 17000 over 5 years so that you can replace your car,
what monthly deposit would be required if you could invest @ 12% compounded monthly?
Explanation :
Here,
FV = 17000
T = 5 years = 60 months
R = 12% yearly = 0.01% monthly
P =?
FV = P / R * [(1+R)^T - 1]
17000 = P × (1.01^60 – 1) ÷ 0.01
17000 = P × 81.6697
So,
P = 17000 / 81.6697
= 208
.............................................
What amount you would need to invest in the annuity if you want to get paid Rs. 20,000 a
year for 20 years when the roi is 5%?
Explanation :
Here,
20000 is to be get paid each year, so the formula is derived from EMI formula:
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 20000 × (1.0520 – 1) ÷ (0.05 × 1.0520)
= 249244
.............................................
Find the present value of quarterly payment of Rs. 250 for 5 years @ 12% compounded
quarterly.
Explanation :
Here,
P = Rs. 250
T = 5 years = 5 × 4 = 20 quarters
R = 12% = 12% ÷ 4 = 0.03% quarterly
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 250 × (1.0320 – 1) ÷ (0.03 × 1.0320)
= 3719
.............................................
A sum of Rs. 25, 000 is borrowed over 8 years. What will be the monthly repayments @
18% compounded monthly?
Explanation :
Here,
PV = Rs. 25000
T = 8 years = 8 × 12 = 96 months
R = 18% = 18% ÷ 12 = 0.015% monthly
PV = P / R * [(1+R)^T - 1]/(1+R)^T
25000 = P × (1.01596 – 1) ÷ (0.015 × 1.01596)
25000 = P × 50.7017
P = 25000 / 50.7017
= 493
.............................................
How much money will a student owe at graduation if she borrows Rs. 3000 per year @ 5%
interest during each of her four years of school?
Explanation :
Here,
P = Rs. 300
T = 4 years
R = 5%
FV = P / R * [(1+R)^T - 1]
FV = 3000 × (1.054 – 1) ÷ 0.05
= 12930
.............................................
A construction company plans to purchase a new earthmover for Rs. 350000 in 5 years.
Determine the annual savings required to purchase the earthmover if the return on
investment is 12%.
Explanation :
Here,
FV = Rs. 350000
T = 5 years
R = 12%
FV = P / R * [(1+R)^T - 1]
350000 = P × (1.125 – 1) ÷ 0.12
350000 = P × 6.3528
P = 350000 / 6.3528
= 55094
.............................................
A man borrowed a certain sum of money & paid it back in 2 years in two equal installments.
If the roi (compound) was 4% p.a. and if he paid back Rs. 676 annually, what sum did he
borrow?
Explanation :
Here,
PV =?
P = Rs. 676
T = 2 years
R = 4% = 0.04
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 676 × (1.042 – 1) ÷ (0.04 × 1.042)
= 1275
.............................................
A sum of Rs. 32800 is borrowed to be paid back in 2 years by two equal annual installments
allowing 5% compound interest. Find the annual payment.
Explanation :
Here,
PV =?
P = Rs. 32800
T = 2 years
R = 5% = 0.05
PV = P / R * [(1+R)^T - 1]/(1+R)^T
32800 = P × (1.052 – 1) ÷ (0.05 × 1.052)
P = 32800 ÷ 1.8594
P = 17640
.............................................
A loan of Rs. 4641 is to be paid back by 4 equal annual installments. The interest is
compounded annually @ 10%. Find the value of each installment.
Explanation :
Here,
PV =?
P = Rs. 4641
T = 4 years
R = 10% = 0.10%
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 4641 × 0.1 × 1.14 ÷ (1.14 – 1)
= 1464
.............................................
A loan of Rs. 1 lac is paid back in 5 equal annual installments. The roi charged is 20%
annually. Find the amount of each loan?
Explanation :
Here,
FV = Rs. 100000
T = 5 years
R = 20% p.a. = 0.2%
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 100000 × 0.2 × 1.25 ÷ (1.25– 1)
= 33438
.............................................
A person wants to borrow Rs. 25000 immediately and another Rs. 20000 after a period of 2
years @ 10% interest. He wants to pay it in monthly installments for 5 years. Calculate the
amount of monthly payment?
Explanation :
Here,
PV of 20000 for 2 years @ 10% = 20000 ÷ 1.0083324 = 16388.07
So, total amount = 25000 + 16388.07 = 41388.07
Now, T = 5 × 12 = 60 months and R = 10% p.a. = 10/1200 = 0.00833
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 41528.93 × 0.00833 × 1.0083360 ÷ (1.0083360 – 1)
= 879
.............................................
You will be receiving Rs. 204000 at the end of each year for the next 20 years. If the current
discount rate for such a stream of cash flow is 10%, find the present value of cash flow.
Explanation :
Here,
P = 204000
R = 10
T = 20
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 1736770
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
X wants to borrow Rs. 25000 immediately and another Rs. 20000 after a period of 2 years
@ 10% roi. He wants to pay it in monthly installments for 5 years. Calculate the amount of
monthly payment.
Explanation :
Here,
First find PV of 20000 for 2 years @ 10%.
Here, t = 2*12 = 24 months and r = 10% ÷ 12 = 0.00833
PV = P / (1+R)^T
So,
PV = 20000 ÷ (1+0.0083)^24
= 16388.07
So, total amount = 25000 + 16388.07 = 41388.07
Now,
P = 41388.07,
R = 10% ÷ 12 = 0.00833,
T = 5 * 12 = 60 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = (41388.07 * 0.00833) * {(1.0083)^60 ÷ (1.0083)^60 – 1)}
= 879
.............................................
A person wants to receive Rs. 1250 every quarter for 5 years @ 12% roi. How much he
should invest now?
Explanation :
Here,
P = 1250
R = 12% quarterly = 3% p.a.
T = 5 yrs = 20 quarters
PV = P / R * [(1+R)^T - 1]/(1+R)^T
So, PV = (1250 ÷ 0.03) * (1.0320 – 1) ÷ 1.0320
= 18597
.............................................
Ranjit borrowed an amount of Rs. 50000 for 8 years @ 18% roi. What shall be monthly
payment?
Explanation :
Here,
P = 50000
R = 18% = 18 % ÷ 12 = 0.015% monthly
T = 8 yrs = 96 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 50000 * 0.015 * 1.01596 ÷ (1.01596 – 1
= 986
.............................................
Ajit wants to receive Rs. 40000 p.a. for 20 years by investing @ 5%. How much he will
have to invest now?
Explanation :
Here,
P = 40000
R = 5% p.a.
T = 20 yrs
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = (40000 ÷ 0.05) * {(1.0520 – 1) ÷ 1.0520}
= 498489
.............................................
Asha wants to receive a fixed amount for 15 years by investing Rs. 9 lacs @ 9% roi. How
much she will receive annually?
Explanation :
Here,
P = 9 lac
R = 9% p.a.
T = 15 yrs
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 900000 * 0.09 * 1.0915 ÷ (1.0915 – 1)
= 111653
.............................................
A firm needs Rs. 170000 to replace its machinery at the end of 5 years. At 12% roi, how
much it should contribute every month?
Explanation :
Here,
FV = 170000
R = 12% p.a. = 0.01% monthly
T = 5 Y = 60 months
(Here, the firm has to contribute monthly, so we have converted rate and time to monthly
equivalent values)
FV, if invested at end of each month / year, is:
FV = P / R * [(1+R)^T - 1]
170000 = P * (1.0160 -1) ÷ 0.01
170000 = P * 81.66967
P = 170000 / 81.66967
= 2082
.............................................
For carrying out his studies, a student borrows Rs. 3 lac from a bank at concessional rate of
5% p.a. for 4 years of his professional course. What is the total amount payable by him at
the end of the 4th year?
Explanation :
Here,
P = 3 lac
R = 5% p.a.
T = 4 yrs
FV = P / R * [(1+R)^T - 1]
FV = 300000*(1.054 – 1) ÷ 0.05
= 1293038
.............................................
X wants to send his daughter to a management school after 5 years and will need onetime
payment of charges amounting to Rs. 7 lac. At 12% roi, how much he should invest
annually?
Explanation :
Here,
FV = 7 lac
R = 12% p.a.
T = 5 yrs
FV = P / R * [(1+R)^T - 1]
700000 = P * (1.125 – 1) ÷ 0.12
700000 = P * 6.352847
P = 110187
.............................................
X opened a recurring account with a bank to deposit Rs. 16000 by the end of each year @
10% roi. How much he would get at the end of 3rd year?
Explanation :
Here,
P = 16000
R = 10% p.a.
T = 3 yrs
FV = P / R * [(1+R)^T - 1]
FV = 16000 * (1.13 – 1) ÷ 0.1
= 52960
.............................................
Alka borrowed Rs. 65600 for 2 years at 5% p.a., to be returned in 2 equal installments.
What is the amount of installment?
Explanation :
Here,
P = 65600
R = 5% p.a.
T = 2 yrs
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 65600 × 0.05 × 1.052 ÷ (1.052 – 1)
= 35280
.............................................
Amrita obtained a loan of Rs. 92820 @ 10%, which he has to pay in 4 equal annual
installments. Calculate the amount of installment?
Explanation :
Here,
P = 92820
R = 10% p.a.
T = 4 yrs
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 92820 × 0.1 × 1.14 ÷ (1.14– 1)
= 29282
.............................................
The compound interest on a sum for 2 years is Rs. 153 and simple interest is 225 for 3
years. What are the roi & the principal amount?
Explanation :
Let,
principal amount = P,
ROI = R,
simple interest = SI,
compound interest = CI
SI for 3 years = 225, so SI for 2 years = 150
CI for 2 years = 153, so difference of Rs. 3 = interest for Rs. 75 (225-150)
So, R = 3/75 *100 = 4%
P = (SI × 100) ÷ (R×T)
= (225×100) ÷ (4×3)
= 1875
.............................................
X purchased a house and payment terms are - Rs. 10 lac immediately and balance Rs. 7.50
lac after 2 years. The roi is 6% p.a. and to be compounded semi-annually. What is the cash
value of the house?
Explanation :
Here,
PV of Rs. 7.50 lac = 750000 ÷ 1.034 = 666370
So, total cash value = 10 lacs + 666370 = Rs. 16,66,370
.............................................
X had to pay certain amount to z and had 2 options - a) to make payment of lump sum
amount of Rs. 120000 immediately or b) to pay Rs. 150000 in 5 years @ 5% p.a. roi
(halfyearly compounding). Which option is more beneficial for x?
a. Option a
b. Option b
c. Both are equal
d. None of the above
Ans - b
Explanation :
If X goes with option b, PV = 150000 ÷ 1.0255×2 = 117180 which is < 120000.
So, option b is more beneficial for X.
.............................................
You will be receiving Rs. 204000 at the end of each year for the next 20 years. If the current
discount rate for such a stream of cash is 10%, find the present value of cash flow.
Explanation :
Here,
Since 204000 is like EMI. So, to find P, we use the formula of EMI
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
204000 = P × 0.1 × 1.1^20 ÷ (1.120 – 1)
204000 = P × 0.1174596
P = 1736767
.............................................
You are receiving Rs. 10000 every year for the next 5 years (at the end of the period) and
you invest each payment @ 5%. How much you would have at the end of the 5-year period?
Explanation :
Here,
P = 10000
R = 5% p.a.
T = 5 yrs
If invested at the end,
FV = P / R * [(1+R)^T - 1]
FV = 10000 × (1.05^5 – 1) ÷ 0.05
= 55256
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
An annuity consists of monthly repayments of Rs. 600 made over 20 years and if rate is
14% monthly. What is the present value of the annuity?
Explanation :
Apply FV formula to get the Answer
Here
R = 14% / 12 = 0.01166
T = 20 × 12 = 240
PV = FV ÷ (1+r)t = 48278
.............................................
Assume that you have a 6% Coupon console bond. The original face value is Rs. 1000 and
the interest rate is 9%. Find the current value of this bond.
Explanation :
Current value of console bond
= Coupon ÷ interest rate
= 60 ÷ 0.09
= Rs. 667
.............................................
A person invested Rs. 100000 in a bank FDR @ 6% p.a. for 1 year. If interest is
compounded on half-yearly basis, the amount payable shall be ......
Explanation :
Here,
P = 100000
R = 6% half-yearly = 3%@ p.a. = 0.03 p.a.
T = 1 yr = 2 half yrs
FV = P * (1 + R)^T
So,
FV = 100000 * (1+0.03)^2
= 106090
.............................................
A person invested Rs. 100000 in a bank FDR @ 6% p.a. for 1 year. If interest is
compounded on quarterly basis, the amount payable shall be ......
Explanation :
Here,
P = 100000
R = 6% quarterly = 0.015% p.a.
T = 1 yr = 4 quarters
FV = P * (1 + R)^T
So,
FV = 100000 * (1+0.015)^4
= 106136
.............................................
A person deposited Rs. 10000 in a post-office scheme @ 8% p.a. with quarterly
compounding, for 2 years. What is the amount payable?
Explanation :
Here,
P = 10000
R = 8% quarterly = 0.02% p.a.
T = 2 Y = 8 quarters
FV = P * (1 + R)^T
So,
FV = 10000 * (1+0.02)^8
= 11717
.............................................
A person borrowed Rs. 10000 from the bank @ 12% p.a. for 1 year, payable on EMI basis.
What is the amount of EMI?
Explanation :
Here,
P = 10000
R = 12% yearly = 0.01% monthly
T = 1 Y = 12 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
So,
EMI = 10000*0.01*(1+0.01)^12 ÷ {(1+0.01)^12 – 1}
= 889
.............................................
A person raised a house loan of Rs. 10 lac @ 12% roi repayable in 10 years. Calculate EMI.
Explanation :
Here,
P = 1000000
R = 12% monthly = 0.01% p.a.
T = 10 Y = 120 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
So,
EMI = 1000000*0.01*(1+0.01)^120 ÷ {(1+0.01)^120 – 1}
= 14347
.............................................
Mr. Raj is to invest Rs. 100000 by end of each year for 5 years @ 5% roi. How much
amount he will receive?
Explanation :
Here,
P = 1000000
R = 5% p.a.
T = 5 Y
FV = P / R * [(1+R)^T - 1]
FV, if invested at end of each year, is:
So,
FV = (100000÷0.05) * {{1+0.05}^5 – 1}
= 552563
.............................................
Mr x is to receive Rs. 10000, as interest on bonds by end of each year for 5 years @ 5% roi.
Calculate the present value of the amount he is to receive.
Explanation :
Here,
P = 10000
R = 5% p.a.
T = 5 Y
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV to be received, if the amount invested at end of each year:
So,
FV = (100000÷0.05) * {(1+0.05)^5 – 1} ÷ (1+0.05)^5
= 43295
.............................................
Population of a town is 100000. The rate of change is 4% p.a. what it will be after 5 years?
Explanation :
Here,
P = 100000
R = 4%
T = 5 yrs
FV = P*(1+R)^T
So,
FV = 10000*(1+0.04)^5
= 121665
.............................................
Population of a town is 100000. The rate of change is 4% p.a. what is was 5 years ago?
Explanation :
Here,
P = 100000
R = 4%
T = 5 yrs
FV = P*(1+R)^-T
So,
FV = 100000*(1+0.04)^-5
= 82193
.............................................
Xyz purchased machinery of Rs. 100000. The rate of depreciation is 10%. At wdv method,
what is the amount of depreciation for 4 years?
Explanation :
Here,
P = 100000
R = 10%
T = 5 yrs
FV = P*(1-R)^T
So,
FV = 100000*(1-0.1)^4
= 65610
So, amount of depreciation
= 100000 – 65610
= 34390
.............................................
Xyz purchased machinery of Rs. 100000. The rate of depreciation is 10%. At wdv method,
what is the average rate of depreciation for 4 years?
Explanation :
Here,
P = 100000
R = 10%
T = 5 yrs
FV = P*(1-R)^T
So,
FV = 100000*(1-0.1)^4
= 65610
So, amount of depreciation
= 100000 – 65610
= 34390
Average rate of depreciation
= (34390 ÷100000) * (4÷10) %
= 13.76%
CAIIB-ABM-IMPORTANT FORMULA
Important Formula
------------------------
Some of these Formula may not be applicable for ABM, but I request all of you to go
through all of them to understand the concepts clear for both ABM and BFM.
1. Raw material Turnover Ratio = Cost of RM used / Average stock of R M
2. SIP Turnover = Cost of Goods manufactured / Average stock of SIP
3. Debt Collection period = No. days or months or Weeks in a year/Debt Turnover Ratio.
4. Average Payment Period = No. days or months or Weeks in a year/Creditors Turnover
Ratio.
5. Inventory Turnover Ratio = Cost of Goods Sold / Average Inventory.
6. Debtors Turnover Ratio = Net Credit Sales / Average Debtors.
7. Creditors Turnover Ratio = Net Credit Purchases / Average Credits.
8. Defensive Interval Ratio = Liquid Assets / Projected Daily Cash Requirement
9. Projected daily cash requirement = Projected operating cash expenses / 365.
10. Debt Equity Ratio = Long Term Debt / Equity.
11. Debt Equity Ratio = Total outside Liability / Tangible Net Worth.
12. Debt to Total Capital Ratio = Total Debts or Total Assets/(Permanent Capital + Current
Liabilities)
13. Interest Coverage Ratio = EBIT / Interest.
14. Dividend Coverage Ratio = N. P. after Interest & Tax / Preferential dividend
15. Gross Profit Margin = Gross Profit / Net Sales * 100
16. Net Profit Margin = Net Profit / Net Sales * 100
17. Cost of Goods Sold Ratio = Cost of Goods Sold / Net Sales * 100.
18. Operating Profit Ratio = Earnings Before Interest Tax / Net Sales * 100
19. Expenses Ratio or Operating Ratio = Expenses / Net Sales * 100
20. Net Profit Ratio = Net Profit After interest and Tax / Net Sales * 100
21. Operating Expenses Ratio = (Administrative + Selling expenses) / Net Sales * 100
22. Administrative Expenses Ratio =(Administrative Expenses / Net Sales ) * 100
23. Selling Expenses Ratio =(Selling Expenses / Net Sales ) * 100
24. Financial Expenses Ratio = ( Financial Expenses / Net Sales ) * 100
25. Return on Assets = Net Profit After Tax / Total Assets.
26. Total Assets = Net Fixed Assets + Net Working Capital.
27. Net Fixed Assets = Total Fixed Assets – Accumulated Depreciation.
28. Net Working Capital = ( CA –CL ) – ( Intangible Assets + Fictitious Assets + Idle Stock
+ Bad Debts )
29. Return on Capital Employed = Net Profit Before Interest and Tax / Average Capital
Employed.
30. Average Capital employed = Equity Capital + Long Term Funds provided by Owners &
Creditors at the beginning & at the end of the accounting period divided by two.
31. Return on Ordinary Share Holders Equity = (NPAT – Preferential Dividends) / Average
Ordinary Share Holders Equity or Net Worth.
32. Earnings Per Share = Net Profit After Taxes and Preferential dividends / Number of
Equity Share.
33. Dividend per Share = Net Profit After Taxes and distributable dividend / Number of
Equity Shares.
34. Dividend Pay Out Ratio = Dividend per Equity Share / Earnings per Equity Share.
35. Dividend Pay Out Ratio = Dividend paid to Equity Share holders / Net Profit available
for Equity Share Holders.
36. Price Earning Ratio = Market Price per equity Share / Earning per Share.
37. Total Asset Turnover = Cost of Goods Sold / Average Total Assets.
38. Fixed Asset Turnover = Cost of Goods Sold / Average Fixed Assets.
39. Capital Turnover = Cost of Goods Sold / Average Capital employed.
40. Current Asset Turnover = Cost of Goods Sold / Average Current Assets.
41. Working Capital Turnover = Cost of Goods Sold / Net Working Capital.
42. Return on Net Worth = ( Net Profit / Net Worth ) * 100
43. DSCR = Profit after Tax & Depreciation + Int. on T L & Differed Credit + Lease
Rentals if any divided by Repayment of Interest & Installments on T L & Differed Credits +
Lease Rentals if any.
44. Factory Cost = Prime cost + Production Overheads.
45. Cost of Goods Sold = Factory Cost + Selling, distribution & administrative overheads
46. Contribution = Sales – Marginal Costs.
47. Percentage of contribution to sales = ( Contribution / Sales ) * 100
48. Break Even Analysis = F / ( 1 – VC / S )
F = Fixed costs, VC = Total variable operating costs & S = Total sales revenue
49. Break Even Margin or Margin of Safety = Sales – Break Even Point / Sales.
50. Cash Break Even = F – N / P – R or F – N / 1 – ( VC / S )
51. BEP = Fixed Costs / Contribution per unit.
52. Sales volume requires = Fixed cost + Required profit / Contribution per unit.
53. BEP in Sales = ( Fixed Costs / Contribution per unit ) * Price per unit.
54. Contribution Sales Ratio = ( Contribution per unit / Sale price per unit ) * 100
55. Level of sales to result in target profit after Tax = (Target Profit) / (1 – Tax rate /
Contribution per unit)
56. Level of sales to result in target profit = (Fixed Cost + Target profit) * sales price per
unit Contribution per unit.
57. Net Present Value = - Co + C1 / (1 + r)
58. Future expected value of a present cash flow = Cash Flow ( 1 + r ) ^ t
59. Present value of a simple future cash flow = Cash Flow / (1 + r) ^ t
60. The Discount Factor = 1 / (1 + r) ^ t
61. Notation used internationally for PV of an annuity is PV ( A, r, n )
62. Notation used internationally for FV of an annuity is FV ( A, r, n )
63. The effective annual rate = ( 1 + r ) ^ t – 1 or (1 + (r / N) ) – 1 )
N = Number of times compounding in a year
64. PV of end of period Annuity = A { (1- (1 / (1+r) ^ n) / r
65. CR = CA : CL
66. Net Worth = CA - CL
67. DER = TL/TNW or debt/equity or TL/equity
68. Price Elasticity of Supply = (% change in quantity supplied/(% change in price)
69. PV = P / R * [(1+R)^T - 1]/(1+R)^T
70. PV = P / (1+R)^T
71. FV = P * (1 + R)^T
72. FV = P*(1-R)^T
73. FV = P / R * [(1+R)^T - 1]
74. FV = P / R * [(1+R)^T - 1] * (1+R)
75. EMI = P * R * [(1+R)^T/(1+R)^T-1)]
76. FV of annuity = A/r ×{(1+r)^n-1}
77. Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
A bond has been issued with a face value of Rs. 1000 at 8% Coupon for 3 years. The
required rate of return is 7%. What is the value of the bond?
Explanation :
Here,
FV = 1000
Coupon Rate (CR) = 0.08
t = 3 yr
R (YTM) = 0.07
Coupon = FV × CR = 80
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So, Value of bond = 1026.25
(Since Coupon rate > YTM, so Bond’s Value > FV)
.............................................
A bond has been issued with a face value of Rs. 20000 at 12% Coupon for 3 years. The
required rate of return is 10%. What is the value of the bond?
Explanation :
Here,
FV = 20000
Coupon Rate (CR) = 0.12
t = 3 yr
R (YTM) = 0.10
Coupon = FV × CR = 2400
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So, Value of bond = 20995
(Since Coupon rate > YTM, so FV < Bond’s Value)
.............................................
A bond has been issued with a face value of Rs. 1000 at 10% Coupon for 3 years. The
required rate of return is 8%. What is the value of the bond if the Coupon amount is payable
on half-yearly basis?
Explanation :
Here,
FV = 1000
CR = 10% half-yearly = 5% p.a.
Coupon = FV × CR = 50
R = 8% yearly = 4% p.a.
t = 3 years
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
= 1052
(Since Coupon rate > YTM, so FV < Bond’s Value)
.............................................
A 10%, 6-years bond, with face value of Rs. 1000 has been purchased by Mr. x for Rs. 900.
What is his yield till maturity?
Explanation :
Here,
FV = 1000
CR = 10%
R (YTM) =?
T = 6 years
Coupon = FV × CR = 100
Bond’s price = 900
Since FV > Bond’s Value, Coupon rate < YTM (based on above three observations)
So, we have to use trial and error method. We have to start with a value > 10 and find the
price until we get a value < 900.
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So,
If YTM = 11%, price =957.69 (> 900, so keep guessing)
If YTM = 12%, price = 917.78 (> 900, so keep guessing)
If YTM = 13%, price = 880.06 (< 900, so stop)
So, YTM must lie between 12 and 13.
So, using interpolation technique,
YTM
= 12 + (917.78 – 900) ÷ (917.78 – 880.06)
= 12 + 17.78 ÷ 37.72
= 12.47%
(Verification: Putting R = 12.47% in bond’s price formula leads to value of 899.80 which is
closest to 900, so YTM = 12.47% is the right answer).
.............................................
Ram purchased two bonds bond-1 & bond-2 with face value of Rs. 1000 each and Coupon
of 8% and maturity of 4 years & 6 years respectively. If YTM is increased by 1%, the %
change in prices of bond-1 & bond-2 would be ......
Explanation :
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
Bond 1:
If YTM is 9%, then bond’s price
= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4
= 967.64
Bond 2:
If YTM is 9%, then bond’s price
= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6
= 955.14
So, % change in price of bond 1
= (1000 – 967.04) ÷ 1000
= 0.03296
= 3.29%
& % change in price of bond 2
= (1000 – 955.14) ÷ 1000
= 0.04486
= 4.48%
.............................................
Monica purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4
years. If YTM is increased by 1%, the change in price of bond would be......
Explanation :
If YTM is 9%, then bond’s price
= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4
= 967.604
So, change in price of the bond
= 1000 - 967.64
= 32.96 decrease
(Since Coupon rate < YTM, so Bond’s Value < FV)
.............................................
Ashwini purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 6
years. If YTM is increased by 1%, the change in price of bond would be......
Explanation :
If YTM is 9%, then bond’s price
= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6
= 955.14
So, change in price of the bond
= 1000 - 955.14
= Rs. 44.86 decrease
(Since Coupon rate < YTM, so Bond’s Value < FV)
.............................................
Priya purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4
years. If YTM is reduced by 2%, the change in price of bond would be......
Explanation :
If YTM = 6%, bond’s price
= [80 × (1.06^4 – 1) ÷ 0.06 + 1000] ÷ 1.06^4
= 1069.30,
So, change in price of the bond
= 1069.30 - 1000
= Rs. 69.30
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
Kumar invested in 10%, 3-year bond of face value of Rs. 1000. The expected market rate is
12%. What is the duration of the bond?
Explanation :
Bond’s Duration = ΣPV×t ÷ ΣP
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
ΣP = {100 × (1.123 -1) ÷ 0.12 + 1000} ÷ 1.123
= 951.6
Here 1 ÷ 1.12 = 0.89286, so a^t = 0.711787
ΣPV × t = 100 × 8.33336 × [0.288213 ÷ 0.10714286 – 3 × 0.711787] + 3000 × 0.711787
= 833.336 × (2.689988 – 2.135361) + 2135.361
= 462.19 + 2135.36 = 2597.55
So, Duration of the Bond
= 2597.55 ÷ 951.6
= 2.73 years
.............................................
Gaurav invested in 12.5%, 5-year bond of face value of Rs. 100. The expected market rate
is 15%. What is the duration of the bond?
Explanation :
Bond’s Duration = ΣPV×T ÷ ΣP
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
ΣP = {12.5 × (1.155 -1) ÷ 0.15 + 100} ÷ 1.155
= 91.6196
Here a = 0.86956 and a^t = 0.497176
So, ΣPV × T = 12.5 × 6.66636 × {0.502824 ÷ 0.13044 – 2.4588} + 248.588
= 116.33046 + 248.588 = 364.92
So, Duration of the Bond
= 364.92 / 91.6196
= 3.98 years
.............................................
Albert purchased 8%, 3 years bond of Rs. 10 lac, with annual interest payment and face
value payable on maturity. The YTM is assumed@ 6%. Calculate the duration and modified
duration.
Explanation :
Bond’s Duration = ΣPV×T ÷ ΣP
ΣP = 1053421
Now, a = 0.943396 and a^t = 0.839619
So, ΣPV×T = 80000 × 16.666 × (0.160381÷0.056604 – 2.518857) + 2518857
= 419370.767 + 25188579
= 2938227.77
So, Duration of the Bond
= 2938227.77 / 1053421
= 2.79 years
& Modified Duration
= Mckauley Duration ÷ (1 + R)
= 2.79 ÷ 1.06
= 2.63
.............................................
Salim purchased 8%, 3 years bond of Rs. 10 lac, with annual interest payment and face
value payable on maturity. The YTM is assumed@ 6%. Calculate % change in the price of
the bond when the decrease in YTM is 100 basis points from 6% to 5% and the duration is
2.79 years and modified duration is 2.63 years.
Explanation :
Percentage change in price of bond
= -MD × Change in Price
= -2.63 × (6% - 5%)
= 2.63%,
That means a fall in YTM by 1% increases the price of the bond by 2.63%.
.............................................
A 12%, 4-year bond of Rs. 100 was purchased by x for Rs. 100. If the market interest rate
increased by 1%, what will the market price?
Explanation :
P = 100
CR = 12%
YTM = 12 + 1 = 13%
So, Price = 97.03
.............................................
Mitalee is to receive Rs. 60000 from bank at the end of 3 years, being the maturity value of
a term deposit. How much he is depositing now, if the interest rate is 10%?
Explanation :
PV
= FV ÷ (1+r)T
= 60000 ÷ 1.3331
= Rs. 45078
.............................................
The cash flow expected from a project is Rs. 700, Rs. 1000 and Rs. 1200 in the 1st, 2nd, &
3rd year. The discounting factor @ 10% roi is 1.10, 1.21 and 1.331. What is the total
present value of these cash flows?
Explanation :
NPV = Σ {C÷ (1+r)T} – 1
Total Present Value
= Σ {C÷ (1+r)T}
= (700 ÷ 1.1) + (1000 ÷ 1.21) + (1200 ÷ 1.331)
= Rs. 2364
.............................................
Priyanka made an investment of Rs. 18000 and he expects a return of Rs. 3000 p.a. For 12
years. What is the present value and net present value of the cash flow @ 10% discount
rate?
Explanation :
PV = 20441
NPV = PV – 18000
= Rs. 2441
.............................................
Current yield on an 8% Rs. 100 bond is 7.5%. The price of the bond is ......
Explanation :
Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
(Here, t = 1
So, price
= (Coupon + Face Value) ÷ (1 + R)
= (8 + 100) ÷ 1.075 = 100.465)
But, since Coupon Interest = Current Yield × Current Market Price
So, Price = 8 ÷ 7.5% = 8000 ÷ 75 = 106.67
.............................................
A 6 year bond is selling at Rs. 9500 with face value of Rs. 10000. The annual Coupon
amount is 800. What is the yield to maturity?
Explanation :
Since Coupon rate = 8% and market price < Face Value, so YTM must be > CR
Let CR be 9%. So, bond’s price = 9551.41 > 9500
Let CR be 10%, so price = 9128.95 < 9500
So, YTM must lie between 9 & 10.
Using interpolation technique,
YTM = 9% + (10-9) % × (9551.41 – 9500) ÷ (9551.41 – 9128.95)
= 9+51.41/422.46
= 9.12%
.............................................
A 15 year bond is trading at Rs. 958 with face value of Rs. 1000. The Coupon rate is 8%.
What is the yield to maturity?
Explanation :
Since trading value < face value, YTM is > CR
At 7%, price = 1091.08 > 958
And at YTM = 9%, price = 919.39 < 958,
so YTM lies somewhere between 7 and 9.
= 7 + (9-7) × (1091.08 – 958) / (1091.08 – 919.39)
= 7 + 2 × 133.08 / 171.69
= 8.5%
.............................................
A 3 year bond with par value Rs. 1000 has Coupon rate 12%. If the required rate of return is
10% and interest is payable semi - annually, find the value of the bond.
Explanation :
Here, interest is calculated semi-annually,
so Coupon = 1000 × 12% ÷ 2 = 60,
YTM = 10%/2 = 0.05,
T = 3 × 2 = 6 years
So, price = 1050
.............................................
The yield on a 6-year bond is 12% while that of 4-year bond is 9%. What should be the
yield on a 2-year bond beginning from now?
Explanation :
(1+12%)^6 = (1+9%)^4 × (1+r)^2
R = 18%
.............................................
A bond is issued with a face value of 1000 that pays a Rs. 25 Coupon semi-annually. Find
its Coupon rate.
Explanation :
Coupon = Face Value × Coupon Rate
25 = 1000 × CR ÷ 2
So, CR = 5%
.............................................
A 2-year bond offers a yield of 6% and a 3-year bond offers a yield of 7.5%. Under the
expectation theory, what should be the yield on a 1-year bond in 2 years?
Explanation :
(1+7.5%)^3 = (1+6%)^2 × (1+r)^1
R = 10.56%
.............................................
Find the price of a zero-Coupon bond maturing in 5 years and has a par value of 1000 and a
required yield of 6%.
Explanation :
Using bond’s price formula, here Coupon = 0 and hence,
Zero-Coupon Bond’s price = Face Value ÷ (1 + R)T = 1000 ÷ 1.065
But, unless otherwise mentioned, the required yield of most zero-Coupon bonds is based on
a semi-annual Coupon payment.
So, Price
= 1000 ÷ 1.0310
= 744
.............................................
A bond with a par-value of Rs. 100 is purchased for 95.92 and it paid a Coupon rate of 5%.
Calculate its current yield.
Explanation :
Coupon = Face value × Coupon Rate
And annual interest paid = Market Price × Current Yield
5 = 95.92 × CY
CY = 0.0521 = 5.21%
.............................................
A zero-Coupon bond has a future value of Rs. 1000 and matures in 2 years and can be
currently purchased for Rs. 925. Calculate its current yield.
Explanation :
Here
1000 = 925 × (1 + r)^2
So,
r = 1.0398 – 1
= 0.0398
= 3.98%
.............................................
You are receiving Rs. 1000 every year for the next 5 years at the beginning of the period
and you invest each payment @ 5%. How much you would at the end of the 5-year period?
Explanation :
Apply FV formula to get the Answer = 5802
.............................................
An annuity consists of monthly repayments of Rs. 600 made over 20 years and if rate is
14% monthly. What is the future value of the annuity?
Explanation :
Apply FV formula to get the Answer
Here
R = 14% / 12 = 0.01166
T = 20 × 12 = 240
FV = 781146
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
The measures of money including Bank deposit with RBI, Demand deposiit with the
banking system, Term deposit of banking systerm, currency with public, and other deposits
with RBI are shown as M0,M1,M2,M3.
1. The liabilities such as current deposits, demand liabilities portion of saving bank, margins
held against letter of credit or bank guarantee, balances in overdue fixed deposits are
included initially, in ......
a. M0
b. M1
c. M2
d. M3
Ans-b
2. The demand deposit of banks are included in ......
a. M0,M1
b. M1,M2
c. M2,M3
d. M1,M2,M3
Ans - b
3. The term deposit of banks are included in ......
a. M0,M1
b. M1,M2
c. M2,M3
d. M1,M2,M3
Ans - c
4. Major portion of which of the following contains, interest free funds and is the most
liquid part of money supply:
a. M0
b. M1
c. M2
d. M3
Ans - a
.....................................................
While releasing the data relating to inflation increased by the Govt, it is observed that
1) The consumer price index based inflation increased to 11% and
2) Whole sale price index based inflation increased to 8%
3) The govt. claims that due to implementation of Banks Bi-partite Settlement, there is
increase in demand of goods and services leading to increase in consumer prices.
4) Further due to increased wages and salaries, there is increase in cost of inputs leading to
increase in whole-sale price index.
Answer the following questions, based on the above information.
1. The inflation caused by the the information given at point no.3 in the question, is not
called as ...... (i) Core inflation, (ii) Demand Pull inflation (iii) Cost-push inflation
a. Only (i) and (ii)
b. Only (i) and (iii)
c. Only (ii) and (iii)
d. (i), (ii) and (iii)
Ans - b
2. The inflation rate of 8%, represented by the whole sale price, is called:
a. Core inflation
b. Headline inflation
c. Demand Pull inflation
d. Cost-push inflation
Ans - b
3. The inflation rate 11% represented by the consumer price, is called:
a. Core inflation
b. Headline inflation
c. Demand Pull inflation
d. Cost-push inflation
Ans - a
4. The inflation caused by the information given at point no.4 in the question, is not called
as ...... (i) Core inflation, (ii) Demand Pull inflation (iii) Cost-push inflation
a. Only (i) and (ii)
b. Only (i) and (iii)
c. Only (ii) and (iii)
d. (i), (ii) and (iii)
Ans - a
.........................................
By using the monetary policy, RBI regulates the money supply, availability of money and
also cost of money i.e.rate of interest. For this purpose, RBI makes use of no. of tools that
include Repo Rate, Bank Rate, Reverse Repo Rate, MSF Rate, SLR, CRR, Market
Stabilization scheme.
Based on this information answer the following question:
1. Which of the following ensures the solvency of commercial banks ?
a. Statutory Liquidity Ratio
b. Market Stablization Scheme
c. Cash Reverse Ratio
d. Repo and Reverse repo transaction
Ans - a
2. Change in which of the following reduce the funds available with banks for lending
purpose ?
a. Repo rate
b. Bank rate
c. Cash reverse Ratio
d. All the above
Ans - c
3. The rate of discount which is used by RBI for rediscounting of commercial instruments
from banks is represented by ......
a. Repo rate
b. Bank rate
c. MSF rate
d. Reverse Repo rate
Ans - b
4. Which of the following is used in the process of neutralizing the effect generated by
foreign exchange flows in india ?
a. Statutory Liquidity Ratio
b. Market Stablization Scheme
c. Cash Reverse Ratio
d. Repo and Reverse repo transaction
Ans - b
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
You are receiving Rs. 10000 every year for the next 5 years (at the beginning of the period)
and you invest each payment @ 5%. How much you would have at the end of the 5-year
period?
Explanation :
Here,
P = 10000
R = 5% p.a.
T = 5 yrs
If invested at the beginning,
FV = P / R * [(1+R)^T - 1] * (1+R)
FV = 55256 × 1.05
= 58019
.............................................
If you wish an annuity to grow to Rs. 17000 over 5 years so that you can replace your car,
what monthly deposit would be required if you could invest @ 12% compounded monthly?
Explanation :
Here,
FV = 17000
T = 5 years = 60 months
R = 12% yearly = 0.01% monthly
P =?
FV = P / R * [(1+R)^T - 1]
17000 = P × (1.01^60 – 1) ÷ 0.01
17000 = P × 81.6697
So,
P = 17000 / 81.6697
= 208
.............................................
What amount you would need to invest in the annuity if you want to get paid Rs. 20,000 a
year for 20 years when the roi is 5%?
Explanation :
Here,
20000 is to be get paid each year, so the formula is derived from EMI formula:
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 20000 × (1.0520 – 1) ÷ (0.05 × 1.0520)
= 249244
.............................................
Find the present value of quarterly payment of Rs. 250 for 5 years @ 12% compounded
quarterly.
Explanation :
Here,
P = Rs. 250
T = 5 years = 5 × 4 = 20 quarters
R = 12% = 12% ÷ 4 = 0.03% quarterly
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 250 × (1.0320 – 1) ÷ (0.03 × 1.0320)
= 3719
.............................................
A sum of Rs. 25, 000 is borrowed over 8 years. What will be the monthly repayments @
18% compounded monthly?
Explanation :
Here,
PV = Rs. 25000
T = 8 years = 8 × 12 = 96 months
R = 18% = 18% ÷ 12 = 0.015% monthly
PV = P / R * [(1+R)^T - 1]/(1+R)^T
25000 = P × (1.01596 – 1) ÷ (0.015 × 1.01596)
25000 = P × 50.7017
P = 25000 / 50.7017
= 493
.............................................
How much money will a student owe at graduation if she borrows Rs. 3000 per year @ 5%
interest during each of her four years of school?
Explanation :
Here,
P = Rs. 300
T = 4 years
R = 5%
FV = P / R * [(1+R)^T - 1]
FV = 3000 × (1.054 – 1) ÷ 0.05
= 12930
.............................................
A construction company plans to purchase a new earthmover for Rs. 350000 in 5 years.
Determine the annual savings required to purchase the earthmover if the return on
investment is 12%.
Explanation :
Here,
FV = Rs. 350000
T = 5 years
R = 12%
FV = P / R * [(1+R)^T - 1]
350000 = P × (1.125 – 1) ÷ 0.12
350000 = P × 6.3528
P = 350000 / 6.3528
= 55094
.............................................
A man borrowed a certain sum of money & paid it back in 2 years in two equal installments.
If the roi (compound) was 4% p.a. and if he paid back Rs. 676 annually, what sum did he
borrow?
Explanation :
Here,
PV =?
P = Rs. 676
T = 2 years
R = 4% = 0.04
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 676 × (1.042 – 1) ÷ (0.04 × 1.042)
= 1275
.............................................
A sum of Rs. 32800 is borrowed to be paid back in 2 years by two equal annual installments
allowing 5% compound interest. Find the annual payment.
Explanation :
Here,
PV =?
P = Rs. 32800
T = 2 years
R = 5% = 0.05
PV = P / R * [(1+R)^T - 1]/(1+R)^T
32800 = P × (1.052 – 1) ÷ (0.05 × 1.052)
P = 32800 ÷ 1.8594
P = 17640
.............................................
A loan of Rs. 4641 is to be paid back by 4 equal annual installments. The interest is
compounded annually @ 10%. Find the value of each installment.
Explanation :
Here,
PV =?
P = Rs. 4641
T = 4 years
R = 10% = 0.10%
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 4641 × 0.1 × 1.14 ÷ (1.14 – 1)
= 1464
.............................................
A loan of Rs. 1 lac is paid back in 5 equal annual installments. The roi charged is 20%
annually. Find the amount of each loan?
Explanation :
Here,
FV = Rs. 100000
T = 5 years
R = 20% p.a. = 0.2%
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 100000 × 0.2 × 1.25 ÷ (1.25– 1)
= 33438
.............................................
A person wants to borrow Rs. 25000 immediately and another Rs. 20000 after a period of 2
years @ 10% interest. He wants to pay it in monthly installments for 5 years. Calculate the
amount of monthly payment?
Explanation :
Here,
PV of 20000 for 2 years @ 10% = 20000 ÷ 1.0083324 = 16388.07
So, total amount = 25000 + 16388.07 = 41388.07
Now, T = 5 × 12 = 60 months and R = 10% p.a. = 10/1200 = 0.00833
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 41528.93 × 0.00833 × 1.0083360 ÷ (1.0083360 – 1)
= 879
.............................................
You will be receiving Rs. 204000 at the end of each year for the next 20 years. If the current
discount rate for such a stream of cash flow is 10%, find the present value of cash flow.
Explanation :
Here,
P = 204000
R = 10
T = 20
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = 1736770
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
X wants to borrow Rs. 25000 immediately and another Rs. 20000 after a period of 2 years
@ 10% roi. He wants to pay it in monthly installments for 5 years. Calculate the amount of
monthly payment.
Explanation :
Here,
First find PV of 20000 for 2 years @ 10%.
Here, t = 2*12 = 24 months and r = 10% ÷ 12 = 0.00833
PV = P / (1+R)^T
So,
PV = 20000 ÷ (1+0.0083)^24
= 16388.07
So, total amount = 25000 + 16388.07 = 41388.07
Now,
P = 41388.07,
R = 10% ÷ 12 = 0.00833,
T = 5 * 12 = 60 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = (41388.07 * 0.00833) * {(1.0083)^60 ÷ (1.0083)^60 – 1)}
= 879
.............................................
A person wants to receive Rs. 1250 every quarter for 5 years @ 12% roi. How much he
should invest now?
Explanation :
Here,
P = 1250
R = 12% quarterly = 3% p.a.
T = 5 yrs = 20 quarters
PV = P / R * [(1+R)^T - 1]/(1+R)^T
So, PV = (1250 ÷ 0.03) * (1.0320 – 1) ÷ 1.0320
= 18597
.............................................
Ranjit borrowed an amount of Rs. 50000 for 8 years @ 18% roi. What shall be monthly
payment?
Explanation :
Here,
P = 50000
R = 18% = 18 % ÷ 12 = 0.015% monthly
T = 8 yrs = 96 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 50000 * 0.015 * 1.01596 ÷ (1.01596 – 1
= 986
.............................................
Ajit wants to receive Rs. 40000 p.a. for 20 years by investing @ 5%. How much he will
have to invest now?
Explanation :
Here,
P = 40000
R = 5% p.a.
T = 20 yrs
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV = (40000 ÷ 0.05) * {(1.0520 – 1) ÷ 1.0520}
= 498489
.............................................
Asha wants to receive a fixed amount for 15 years by investing Rs. 9 lacs @ 9% roi. How
much she will receive annually?
Explanation :
Here,
P = 9 lac
R = 9% p.a.
T = 15 yrs
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 900000 * 0.09 * 1.0915 ÷ (1.0915 – 1)
= 111653
.............................................
A firm needs Rs. 170000 to replace its machinery at the end of 5 years. At 12% roi, how
much it should contribute every month?
Explanation :
Here,
FV = 170000
R = 12% p.a. = 0.01% monthly
T = 5 Y = 60 months
(Here, the firm has to contribute monthly, so we have converted rate and time to monthly
equivalent values)
FV, if invested at end of each month / year, is:
FV = P / R * [(1+R)^T - 1]
170000 = P * (1.0160 -1) ÷ 0.01
170000 = P * 81.66967
P = 170000 / 81.66967
= 2082
.............................................
For carrying out his studies, a student borrows Rs. 3 lac from a bank at concessional rate of
5% p.a. for 4 years of his professional course. What is the total amount payable by him at
the end of the 4th year?
Explanation :
Here,
P = 3 lac
R = 5% p.a.
T = 4 yrs
FV = P / R * [(1+R)^T - 1]
FV = 300000*(1.054 – 1) ÷ 0.05
= 1293038
.............................................
X wants to send his daughter to a management school after 5 years and will need onetime
payment of charges amounting to Rs. 7 lac. At 12% roi, how much he should invest
annually?
Explanation :
Here,
FV = 7 lac
R = 12% p.a.
T = 5 yrs
FV = P / R * [(1+R)^T - 1]
700000 = P * (1.125 – 1) ÷ 0.12
700000 = P * 6.352847
P = 110187
.............................................
X opened a recurring account with a bank to deposit Rs. 16000 by the end of each year @
10% roi. How much he would get at the end of 3rd year?
Explanation :
Here,
P = 16000
R = 10% p.a.
T = 3 yrs
FV = P / R * [(1+R)^T - 1]
FV = 16000 * (1.13 – 1) ÷ 0.1
= 52960
.............................................
Alka borrowed Rs. 65600 for 2 years at 5% p.a., to be returned in 2 equal installments.
What is the amount of installment?
Explanation :
Here,
P = 65600
R = 5% p.a.
T = 2 yrs
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 65600 × 0.05 × 1.052 ÷ (1.052 – 1)
= 35280
.............................................
Amrita obtained a loan of Rs. 92820 @ 10%, which he has to pay in 4 equal annual
installments. Calculate the amount of installment?
Explanation :
Here,
P = 92820
R = 10% p.a.
T = 4 yrs
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
EMI = 92820 × 0.1 × 1.14 ÷ (1.14– 1)
= 29282
.............................................
The compound interest on a sum for 2 years is Rs. 153 and simple interest is 225 for 3
years. What are the roi & the principal amount?
Explanation :
Let,
principal amount = P,
ROI = R,
simple interest = SI,
compound interest = CI
SI for 3 years = 225, so SI for 2 years = 150
CI for 2 years = 153, so difference of Rs. 3 = interest for Rs. 75 (225-150)
So, R = 3/75 *100 = 4%
P = (SI × 100) ÷ (R×T)
= (225×100) ÷ (4×3)
= 1875
.............................................
X purchased a house and payment terms are - Rs. 10 lac immediately and balance Rs. 7.50
lac after 2 years. The roi is 6% p.a. and to be compounded semi-annually. What is the cash
value of the house?
Explanation :
Here,
PV of Rs. 7.50 lac = 750000 ÷ 1.034 = 666370
So, total cash value = 10 lacs + 666370 = Rs. 16,66,370
.............................................
X had to pay certain amount to z and had 2 options - a) to make payment of lump sum
amount of Rs. 120000 immediately or b) to pay Rs. 150000 in 5 years @ 5% p.a. roi
(halfyearly compounding). Which option is more beneficial for x?
a. Option a
b. Option b
c. Both are equal
d. None of the above
Ans - b
Explanation :
If X goes with option b, PV = 150000 ÷ 1.0255×2 = 117180 which is < 120000.
So, option b is more beneficial for X.
.............................................
You will be receiving Rs. 204000 at the end of each year for the next 20 years. If the current
discount rate for such a stream of cash is 10%, find the present value of cash flow.
Explanation :
Here,
Since 204000 is like EMI. So, to find P, we use the formula of EMI
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
204000 = P × 0.1 × 1.1^20 ÷ (1.120 – 1)
204000 = P × 0.1174596
P = 1736767
.............................................
You are receiving Rs. 10000 every year for the next 5 years (at the end of the period) and
you invest each payment @ 5%. How much you would have at the end of the 5-year period?
Explanation :
Here,
P = 10000
R = 5% p.a.
T = 5 yrs
If invested at the end,
FV = P / R * [(1+R)^T - 1]
FV = 10000 × (1.05^5 – 1) ÷ 0.05
= 55256
CAIIB - ABM- CASE STUDIES / NUMERICAL QUESTIONS
An annuity consists of monthly repayments of Rs. 600 made over 20 years and if rate is
14% monthly. What is the present value of the annuity?
Explanation :
Apply FV formula to get the Answer
Here
R = 14% / 12 = 0.01166
T = 20 × 12 = 240
PV = FV ÷ (1+r)t = 48278
.............................................
Assume that you have a 6% Coupon console bond. The original face value is Rs. 1000 and
the interest rate is 9%. Find the current value of this bond.
Explanation :
Current value of console bond
= Coupon ÷ interest rate
= 60 ÷ 0.09
= Rs. 667
.............................................
A person invested Rs. 100000 in a bank FDR @ 6% p.a. for 1 year. If interest is
compounded on half-yearly basis, the amount payable shall be ......
Explanation :
Here,
P = 100000
R = 6% half-yearly = 3%@ p.a. = 0.03 p.a.
T = 1 yr = 2 half yrs
FV = P * (1 + R)^T
So,
FV = 100000 * (1+0.03)^2
= 106090
.............................................
A person invested Rs. 100000 in a bank FDR @ 6% p.a. for 1 year. If interest is
compounded on quarterly basis, the amount payable shall be ......
Explanation :
Here,
P = 100000
R = 6% quarterly = 0.015% p.a.
T = 1 yr = 4 quarters
FV = P * (1 + R)^T
So,
FV = 100000 * (1+0.015)^4
= 106136
.............................................
A person deposited Rs. 10000 in a post-office scheme @ 8% p.a. with quarterly
compounding, for 2 years. What is the amount payable?
Explanation :
Here,
P = 10000
R = 8% quarterly = 0.02% p.a.
T = 2 Y = 8 quarters
FV = P * (1 + R)^T
So,
FV = 10000 * (1+0.02)^8
= 11717
.............................................
A person borrowed Rs. 10000 from the bank @ 12% p.a. for 1 year, payable on EMI basis.
What is the amount of EMI?
Explanation :
Here,
P = 10000
R = 12% yearly = 0.01% monthly
T = 1 Y = 12 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
So,
EMI = 10000*0.01*(1+0.01)^12 ÷ {(1+0.01)^12 – 1}
= 889
.............................................
A person raised a house loan of Rs. 10 lac @ 12% roi repayable in 10 years. Calculate EMI.
Explanation :
Here,
P = 1000000
R = 12% monthly = 0.01% p.a.
T = 10 Y = 120 months
EMI = P * R * [(1+R)^T/(1+R)^T-1)]
So,
EMI = 1000000*0.01*(1+0.01)^120 ÷ {(1+0.01)^120 – 1}
= 14347
.............................................
Mr. Raj is to invest Rs. 100000 by end of each year for 5 years @ 5% roi. How much
amount he will receive?
Explanation :
Here,
P = 1000000
R = 5% p.a.
T = 5 Y
FV = P / R * [(1+R)^T - 1]
FV, if invested at end of each year, is:
So,
FV = (100000÷0.05) * {{1+0.05}^5 – 1}
= 552563
.............................................
Mr x is to receive Rs. 10000, as interest on bonds by end of each year for 5 years @ 5% roi.
Calculate the present value of the amount he is to receive.
Explanation :
Here,
P = 10000
R = 5% p.a.
T = 5 Y
PV = P / R * [(1+R)^T - 1]/(1+R)^T
PV to be received, if the amount invested at end of each year:
So,
FV = (100000÷0.05) * {(1+0.05)^5 – 1} ÷ (1+0.05)^5
= 43295
.............................................
Population of a town is 100000. The rate of change is 4% p.a. what it will be after 5 years?
Explanation :
Here,
P = 100000
R = 4%
T = 5 yrs
FV = P*(1+R)^T
So,
FV = 10000*(1+0.04)^5
= 121665
.............................................
Population of a town is 100000. The rate of change is 4% p.a. what is was 5 years ago?
Explanation :
Here,
P = 100000
R = 4%
T = 5 yrs
FV = P*(1+R)^-T
So,
FV = 100000*(1+0.04)^-5
= 82193
.............................................
Xyz purchased machinery of Rs. 100000. The rate of depreciation is 10%. At wdv method,
what is the amount of depreciation for 4 years?
Explanation :
Here,
P = 100000
R = 10%
T = 5 yrs
FV = P*(1-R)^T
So,
FV = 100000*(1-0.1)^4
= 65610
So, amount of depreciation
= 100000 – 65610
= 34390
.............................................
Xyz purchased machinery of Rs. 100000. The rate of depreciation is 10%. At wdv method,
what is the average rate of depreciation for 4 years?
Explanation :
Here,
P = 100000
R = 10%
T = 5 yrs
FV = P*(1-R)^T
So,
FV = 100000*(1-0.1)^4
= 65610
So, amount of depreciation
= 100000 – 65610
= 34390
Average rate of depreciation
= (34390 ÷100000) * (4÷10) %
= 13.76%
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