CA FOUNDATION - MATHEMATICS

TIME VALUE OF MONEY

Simple Interest
Simple interest is charged on the principal amount and hence it is same for every year.

A = Amount, P = principal, n = number of years, R = interest rate

Notes:
• If rate of interest is known, then sum of money will double itself in 100/r years.
• If number of years is known, then sum of money will double itself @ 100/n %.
• A sum of money will become “n” times in years.

Example:
In how many years a sum of money @10% p.a. SI will become (a) double, (b) triple,
(c) N times.

(a) Double (b) Triple (c) N times

• If the sum of money becomes “n1” times in T1 years and “n2” times in T2 years, then
the ratio of their times is: .

Compound Interest
• In case of compound interest, the interest is calculated on the amount of the
succeeding years, i.e., principal keeps changing every year.

• Here interest on interest is also earned, thus money grow faster when
Compounding is done

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• If P is the principal, n = number of years for which interest is calculated and “i”
(R/100) is the rate of interest, then, the amount A after n years will be given
by:
A=P(1+i)n
• In case of depreciation by diminishing balance method (WDV), if C = Cost of
the machinery, I = rate of depreciation per annum and n = effective life of the
machinery, then the depreciated value D after n years is :
D = C (1 - i)n
D is also known as the scrap value of the machinery.
• Compound Interest thus would be calculated as follows:

• Depending upon the compounding style of interest rate, the effective formula
for calculating Amount would be as follows:

Half Yearly or Semi Annually Quarterly Monthly

• When differential interest rates are charged (i1, i2, i3,... ... in), then:

• Relationship between CI and SI
a) For the first year, CI = SI, i.e. for the first year difference is zero.
b) For two years, CI – SI = Pi2
c) For three years, CI – SI = Pi2(i + 3)

Notes:
1. A sum of money will double itself in approximately 72/r years (known as Rule
72), where r is the rate of interest per annum.

2. A sum of money will triple itself in approximately 114/r (known as Rule 114),
where r is the rate of interest per annum.

3. If a sum of money becomes “n” times in “t” years, then, it will become nm times
in “mt” years.
Example: If sum of money doubles itself in 3 years, then it will be 8 times (23)
in 3x3 = 9 years at CI.

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Concept of Effective Rate of Interest

1. When the compounding is done more than once a year, then, the net annual
rate of interest is found to be slightly higher than the given annual rate of
interest.

2. This new rate of interest is known as the effective rate of interest and the given
annual rate is called the nominal rate of interest.

3. Effective rate of interest is denoted by E and is given by the formula:

Where “i” is rate of interest, converted monthly, quarterly, half yearly and n is
the number of conversion period per annum.

4. Effective rate of interest are particularly useful in making investment decisions

when various options are given with differential interest rates.

5. Amongst various investment options, we shall choose that investment option,

where effective rate of interest is maximum.

Concept of Present Value

Present Value is defined as the present worth of the money that would yield an
amount A after n years at a specified rate of interest i.

Annuities
• Annuity is defined as a series of payments (usually equal) which are made at
regular intervals of time (usually a year).

• The period for which the payment continues is called the status or the term of
the annuity.

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• Unless otherwise stated, the first payment will fall due at the end of every
year. This is known as “Ordinary Annuity”.

• When the payment falls due at the beginning of every year, i.e., immediately,
it is called “Immediate Annuity”.

• When the status or term of the annuity is not fixed, i.e., the payment is to be
continued for an indefinite period, these are known as “Perpetual Annuity or
Perpetuity”.

• Hence forth, we shall maintain the following notation throughout. The regular
annual payment i.e., annuity = P, rate of interest = “i” and the period for which
payment is made = n (status or term of the annuity).

• The amount of the ordinary annuity is given by:

• The amount of immediate annuity is obtained by multiplying amount obtained

for ordinary annuity by (1 + i); hence the formula becomes:

• Note:
1. When half yearly or quarterly or monthly payment is “P”, in such a
case change “i” to i/2 or i/4 or i/12 and change “n” to 2n or 4n or 12n
respectively.

2. When half yearly, quarterly or monthly rate of interest is “i”, in such a case,
change P to P/2, P/4 or P/12 and change n to 2n or 4n or 12n respectively.

• The present value of an annuity payable over a period of n years is defined as

the sum of the present value of all the future payments.

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• The present value of an ordinary annuity is represented by V and given as

follows:

• If the term of the annuity is n years, then for evaluating the present value of
the immediate annuity, first calculate the present value of the annuity for (n–1)
years and then add to it the initial or first payment.

• Present value of the perpetual annuity is given by,

V = P/i

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CLASSWORK SECTION

SIMPLE INTEREST

1. How much interest will be earned on Rs. 4000 at 6% p.a. simple interest for 2 yrs?
(a) 450 (b) 480 (c) 500 (d) 540

2. A deposited 1,00,000 in a bank for 2 years with the interest at 5.5% p.a. What will
be the first value of investment?
(a) 1,00,000 (b) 1,11,000 (c) 1,20,000 (d) 1,30,000

3. Find rate of interest if the amount owed after 6 months is 2100, borrowed amount
being Rs. 2000.
(a) 10% (b) 8% (c) 9% d 11%

4. P = 5000, N = 1, I = 300, R will be

(a) 5% (b) 4% (c) 6% (d) none

5. 46875 was lent out at SI and at the end of 1 yr 8 months, total amount was 50000.
Find rate of int per annum?
(a) 2% (b) 4% (c) 6% (d) 8%

6. Sum required to earn quarterly interest of 3600 at 18% p.a. is

(a) 50,000 (b) 60,000 (c) 80,000 (d) none

7. In how much time would SI on a certain sum be 0.125 times the principal at 10%
p.a.?
(a) 1 ¼ years (b) 1.5 years (c) 1 ¾ years (d) 2 ¼ years

8. A sum of 3402 amounts to 6804 on 20 yrs. What sum will amount to 5200 in 6 yrs
at same rate?
(a) 3000 (b) 4000 (c) 5000 (d) 600

9. 30000 is invested in two parts : partly at 10% p.a. and partly at 15% p.a. Total
interest earned is 3300. How much is invested at lower rate?
(a) 20000 (b) 24000 (c) 26000 (d) 28000

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10. A bike is purchased by making a down payment of 15000 and balance to be paid
alongwith interest at 5% p.a. for 2 yrs. Total amount paid is 28200. Find cash price
of the bike.
(a) 28000 (b) 26000 (c) 27000 (d) 25000

11. A certain sum amounts to 7400 in 3 yrs and 8600 in 4 yrs. Find the sum and rate of
interest
(a) 3800, 31.57% (b) 3,000, 25%
(c) 3,500, 20% (d) none

12. A certain sum doubles itself in 20 yrs. In how many years it will become 7 times
(a) 100 (b) 120 (c) 140 (d) none

13. Mr. X takes loan of 7000 for 8 yrs. After 3 yrs he taken 3000 more. Total interest paid
at the end of 8 years is 3550. Find the rate of interest.
(a) 4% p.a. (b) 5% p.a. (c) 6% p.a. (d) none

PAST EXAM QUESTIONS

14. ` 8,000 becomes ` 10,000 in two years at simple interest. The amount that will
become ` 6,875 in 3 years at the same rate of interest is:
(a) ` 4,850 (b) ` 5,000 (c) ` 5,500 (d) ` 5,275

15. The rate of simple interest on a sum of money is 6% p.a. for first 3 years, 8% p.a. for
the next five years and 10% p.a. for the period beyond 8 years. If the simple interest
accrued by the sum for a period for 10 years is ` 1,560. The sum is:
(a) ` 1,500 (b) ` 2,000 (c) ` 3,000 (d) ` 5,000

16. A sum of money doubles itself in 10 years. The number of years it would treble itself
is :
(a) 25 years (b) 15 years (c) 20 years (d) none

17. A certain sum of money amounts to ` 6,300 in two years and ` 7,875 in three years
nine months at simple interest. Find the rate of interest per annum.
(a) 20% (b) 18% (c) 15% (d) 10%

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18. If ` 1,000 be invested at interest rate of 5% and the interest be added to the principal
every 10 years, then the number of years in which it will amount to ` 2,000 is:

2 1
(a) 16 years (b) 16 years
3 4

2
(c) 16 years (d) 16 years
3
1
19. Two equal sums of money were lent at simple interest at 11% p.a. for 3 2 years and
1
4 2 years respectively. If the difference in interests for two periods was ` 412.50,
then each sum is:
(a) ` 3,250 (b) ` 3,500 (c) ` 3,750 (d) ` 4,350

20. Find the numbers of years in which a sum doubles itself at the rate of 8% per
annum.
1 1
(a) 11 (b) 12
2 2

1 1
(c) 9 (d) 13
2 2

21. What is the rate of simple interest if a sum of money amounts to ` 2,784 in 4 years
and ` 2,688 in 3 years?
(a) 1% p.a. (b) 4% p.a. (c) 5% p.a. (d) 8% p.a.

22. If a simple interest on a sum of money at 6% p.a. for 7 years is equal to twice of
simple interest on another sum for 9 years at 5% p.a. The ratio will be
(a) 2 : 15 (b) 7 : 15 (c) 15 : 7 (d) 1 : 7

23. If the simple interest on ` 1,400 for 3 years is less than the simple interest on
` 1,800 for the same period by ` 80, then the rate of interest is
(a) 5.67% (b) 6.67% (c) 7.20% (d) 5.00%

4
24. The S.I. on a sum of money is of the principal and the no. of years is equal to the
9
rate of interest per annum. Find the rate of interest per annum?
(a) 5% (b) 20/3% (c) 22/7% (d) 6%

25. Simple interest on ` 2,000 for 5 months at 16% p.a. is _____

(a) ` 133.33 (b) ` 133.26 (c) ` 134.00 (d) ` 132.09

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26. Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating
the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is
`9,774. Find the period for which the sum was invested:
(a) 7 years (b) 5.8 years (c) 6 years (d) 8 years

27. What principal will amount to ` 370 in 6 years at 8% p.a. at simple interest?
(a) ` 210 (b) ` 250 (c) ` 310 (d) ` 350

28. If a sum triples in 15 years at simple rate of interest, the rate of interest per annum
will be:
(a) 13.0% (b) 13.3% (c) 13.5% (d) 18.0%

29. A certain sum of money was invested at simple rate of interest for three years. If
the same has been invested at a rate that was seven percent higher, the interest
amount would have been ` 882 more. The amount of sum invested is:
(a) ` 12,600 (b) ` 6,800 (c) ` 4,200 (d) ` 2,800

30. A sum of ` 44,000 is divided into three parts such that the corresponding interest
earned after 2 years, 3 years and 6 years may be equal. If the rates of simple
interest are 6% p.a., 8% p.a. and 6% p.a. respectively, then the smallest part of the
sum will be :
(a) ` 4,000 (b) ` 8,000 (c) ` 10,000 (d) ` 12,000

31. A person lends ` 6,000 for 4 years and ` 8,000 for 3 years at simple interest. If he
gets ` 2,400 as total interest, the rate of interest is:
(a) 5% (b) 4% (c) 6% (d) 7%

32. A person borrows ` 5,000 for 2 years at 4% per annual simple interest. He
1
immediately lends to another person at 6 %. Per annual for 2 years find his gain
4
in the transaction for year:
(a) ` 112.50 (b) ` 225 (c) ` 125 (d) ` 107.50

33. A certain money doubles itself in 10 years when deposited on simple interest. If
would triple itself in
(a) 20 years (b) 15 years (c) 25 years (d) 30 years

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34. A certain sum of money Q was deposited for 5 year and 4 months at 4.5% simple
interest and amounted to ` 248, then the value of Q is
(a) ` 200 (b) ` 210 (c) ` 220 (d) ` 240

35. A man invests an amount of ` 15,860 in the names of his three sons A, B and C in
such a way that they get the same SI after 2, 3 and 4 years respectively. If the rate
of interest is 5%, then the ration of amount invested in the name of A, B and C is
(a) 6 : 4 : 3 (b) 3:4:6 (c) 30 : 12 : 5 (d) none of these

COMPOUND INTEREST

36. Find amount for a sum of 4000 at 8% p.a. for 5 yrs compounded annually?
(a) 5877 (b) 6577 (c) 8577 (d) 5677

37. Find C–I for a sum of 8000 at 4% p.a. for 6 yrs compounded half yearly?
(a) 2146 (b) 2416 (c) 2164 (d) 2641

38. Find amount and C–I for a sum of 6000 at 12% p.a. for 3 years compounded
quarterly?
(a) 8554.5, 2554.5 (b) 7554.5,1554.5
(c) 9554.5, 3554.5 (d) 6554.5,554.5

39. Find amount for a sum of 10000 at 6% p.a. for 2 years compounded monthly?
(a) 12171 (b) 11712 (c) 11271 (d) 12117

40. Find present value of 10000 due in 2 yrs at 5% p.a. compound interest paid annually?
(a) 9050 (b) 9070 (c) 9080 (d) 9090

41. Find present value of 20000 due in 3 yrs at 6% p.a. C–I paid half yearly?
(a) 16570 (b) 16500 (c) 16750 (d) 16075

42. A machinery is depreciated at 10% p.a. for 3 yrs costing Rs. 50000.Find scrap value?
(a) 36400 (b) 36450 (c) 36500 (d) 36550

43. Find depreciation if machinery worth 12000 is depreciated at 6% p.a. for 4 yrs?
(a) 2631.8 (b) 2613.8 (c) 2361.8 (d) 2316.8

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44. A machinery worth 10000 is depreciated at the rate of 10% p.a. for first 3 yrs. 8%
p.a. for next 2 yrs. Find its value after 5 yrs.
(a) 5170.25 (b) 7170.25 (c) 6170.25 (d) 8170.25

45. An investment of 20000 sums on interest of 6% p.a. for first 4 yrs 5% p.a. for next 3
yrs and 4% p.a. for next 2 yrs. Find value of investment after 9 yrs where interest is
compound annually
(a) 31441.62 (b) 31614.62 (c) 31416.62 (d) 31641.62

46. Difference between C–I and SI at 5% p.a. for 2 yrs on a sum of 6000 is
(a) 10 (b) 12 (c) 15 (d) 18

47. Difference between CI and SI at 8% p.a. for 3 yrs on a sum of 50000 is

(a) 958.6 (b) 985.6 (c) 968.6 (d) 995.6

48. Difference between CI and SI on 10000 at 5% p.a. for 4 yrs is

(a) 150 (b) 155 (c) 160 (d) 165

49. A sum of money at 5% p.a. CI double in

(a) 14 yrs (approx.) (b) 16 yrs (approx.)
(c) 18 yrs (approx.) (d) 19 yrs (approx.)

50. In how many years a sum of money trebles at 5% p.a. CI payable on half yearly
basis
(a) 20 yrs 3 months (b) 21 yrs 3 months
(c) 22 yrs 3 months (d) 24 yrs 3 months

51. A sum at a certain rate of interest compounded annually doubles in 5 yrs. In how
many yrs will it become 8 times
(a) 10 (b) 15 (c) 18 (d) 20

PAST EXAM QUESTIONS

52. The difference between the simple and compound interest on a certain sum for 3
year at 5% p.a. is ` 228.75. The compound interest on the sum for 2 years at 5%
p.a. is
(a) ` 3,175 (b) ` 3,075 (c) ` 3,275 (d) ` 2,975

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53. In what time will ` 3,90,625 amount to ` 4,56,976 at 8% per annum, when the
interest is compounded semi-annually?
(a) 2 years (b) 4 years (c) 5 years (d) 7 years

54. How long will ` 12,000 take to amount to ` 14,000 at 5% p.a. converted quarterly?
[Given : (1.0125)12.4 = 1.1666]
(a) 3 years (b) 3.1 years (c) 13.5 years (d) 12.4 years

55. The annual birth and death rates per 1000 are 39.4 and 19.4 respectively. The
number of years in which the population will be doubled assuming there is no
immigration or emigration is:
(a) 35 years (b) 30 years (c) 25 years (d) none of these

56. A person deposited ` 5000 in a bank. The deposit was left to accumulate at 6%
compounded quarterly for the first five years and at 8% compounded semi-annually
for the next eight years. The compound amount at the end of 13 years is:
(a) ` 12621.50 (b) ` 12613.10 (c) ` 13613.10 (d) none

57. The difference between compound interest and simple interest on a certain sum for
2 years @10% p.a. is ` 10. Find the sum:
(a) ` 1,010 (b) ` 1,095 (c) ` 1,000 (d) `990

58. A sum amount to ` 1,331 at a principal of ` 1,000 at 10% compounded annually.

Find the time.
(a) 3.31 years (b) 4 years (c) 3 years (d) 2 years

59. At what % rate of compound interest (C.I) will a sum of money become 16 times in
four years, if interest is being calculated compounding annually:
(a) r = 100% (b) r = 10% (c) r = 200% (d) r = 20%

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60. Mr. X invests ‘P’ amount at simple interest rate 10% and Mr. Y invests ‘Q’ amount
at compound interest rate 5% compounded annually. At the end of two years both
get the same amount of interest, then the relation between two amounts P and Q
is given by

(a) (b)

(c) (d)

61. A sum of money compounded annually becomes ` 1,140 in two years and ` 1,710
in three years. Find the rate of interest per annum.
(a) 30% (b) 40% (c) 50% (d) 60%

62. A sum of money invested of compound interest doubles itself in four years. It
becomes 32 times of itself at the same rate of compound interest in
(a) 12 years (b) 16 years (c) 20 years (d) 24 years

63. A compound interest on a sum for 2 years is ` 30 more than the simple interest at
the rate of 5% per annum then the sum is
(a) ` 11,000 (b) ` 13,000 (c) ` 12,000 (d) ` 15,000

64. If compound interest on any sum at the rate of 5% for two years is ` 512.50 then
the sum would be:
(a) ` 3,000 (b) ` 4,000 (c) ` 5,000 (d) ` 6,000

65. If compound interest on a sum for 2 years at 4% per annum is ` 102, then the
simple interest on the same sum for the same period at the same rate will be
(a) ` 99 (b) ` 101 (c) ` 100 (d) ` 95

EFFECTIVE RATE OF INTEREST

66. Effective annual rate of interest compounding to a nominal rate of 6% p.a payable
half yearly is
(a) 6.07 (b) 6.08 (c) 6.09 (d) none

67. Effective rate of interest of 8% p.a. converted monthly is

(a) 8% (b) 8.34% (c) 8.43% (d) none

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68. Which is a better investment?

(i) 9% p.a. compounded half yrly.
(ii) 9.23% p.a. S.I.
(a) (i) (b) (ii) (c) both (d) none

ANNUITY (FUTURE VALUE)

69. The amount of annuity of 6,000 payable at the end of each 3 months for 4 years
compounded at 8% p.a.
(a) 111836 (b) 110836 (c) 112836 (d) 113836

70. Mr. Beans deposits 25,000 at the end of every year at 12% p.a. C.I. What amount
he would receive at the end of 10 yrs?
(a) 438178 (b) 438718 (c) 438817 (d) 438781

71. The amount of annuity of Rs. 2000 payable at the end of each year for 5 years at
8% p.a. is
(a) 11733.86 (b) 14502.6 (c) 21005.8 (d) 16721.31

72. Mr. Yash wants 10,00,000 at the end of 5 yrs. Its opens recurring account with post
office at 10% p.a. C.I compound monthly. What money should be deposited at the
end of every month?
(a) 12914 (b) 19214 (c) 14219 (d) 11294

73. A company requires 20,00,000 at the end of 10 yrs to replace one of its assets. It is
decided to create a sinking fund by investing a fixed amount every year in securities
which gives 10% CI. Yearly investment is
(a) 124590 (b) 125490 (c) 154290 (d) 145290

74. A company issued 10% cumulative debentures of 100 each 5000 cumulative
debentures are to be redeemed with 10% of interest for 5 yrs. For this a Sinking
Fund is created and invested at 12% rate of C.I. Sum to be transferred every year to
sinking fund is
(a) 805500 (b) 126834.64 (c) 207382 (d) 126755

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75. The value of the amount at the end of 12 years of an annuity of 1200 payable at
the beginning of each year for 12 yrs at 8% p.a. C.I is
(a) 26879.32 (b) 3432.11 (c) 24594.35 (d) none

76. Mr. Piyush invests 10000 every year starting from today for next 10 yrs rate of
interest is 8% p.a. Find F.V of annuity.
(a) 156484.875 (b) 156454.875 (c) 156494.875 (d) none

77. A machine costing 5,20,000 with an estimated life of 25 years. A sinking fund is
created to replace it by new model at 25% higher cost after 25 years with a scrap
value realization of 25000. What amount should be set aside every year if sinking
fund investment at 3.5% C.I p.a.?
(a) 16000 (b) 16500 (c) 16050 (d) 16005

78. Ratan aged 45 wishes his wife Ratna to have 40 lacs at his death. His expectation of
life is another 30 years and he starts making equal annual investments commencing
now at 3% p.a., how much should he invest annually?
(a) 84077 (b) 81628 (c) 84450 (d) none

ANNUITY (PRESENT VALUE)

79. A loan of 30,000 at the interest rate of 6% compounded annually is to be amortized
by equal payments at the end of each year for 5 years. Find annual payment.
(a) 6121.89 (b) 7121.89 (c) 8121.89 (d) 9121.89

80. Present value of an annuity which pays 200 at the end of each 3 months for 10
years, assuming money to be worth 5% converted quarterly.
(a) 3809.20 (b) 3109.60 (c) 6265.38 (d) none

81. Pravin buys a house paying Rs. 50,000 in cash and balance in 20 installments of Rs.
8,000 each at the end of each year. If interest is at 16% p.a., how much he should
have paid if had purchased it cash down.
(a) 85250 (b) 94730 (c) 97430 (d) 87589

82. P.V. of an annuity of Rs. 80 made at the end of each 6 months forever, if money
worth 4% p.a. is compounded semi-annually
(a) 2000 (b) 3000 (c) 4000 (d) 5000

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83. A man purchased house valued at 3,00,000 by making a payment of 2,00,000 at the
time of purchase and agreed to pay balance with interest at 12% p.a. compounded
half yearly in 20 equal half yearly installments. If first installment is paid after 6
months from the date of purchase then amount of each installment is
(a) 8719 (b) 8679 (c) 7719 (d) 8769

84. A car is purchased for 1,00,000 down payment and an installment of 6,500 per
month for 3 years. If the rate of interest is 15% p.a. compound monthly, cash price
is
(a) 87507 (b) 187507 (c) 287507 (d) 387507

85. John wants to create a fund to donate 1800 every month to a deprived family. Rate
of unit is 12% p.a. Find amount to be deposited
(a) 360000 (b) 180000 (c) 90000 (d) none

86. A company borrows 10000 on condition to repay it with C.I. at 5% p.a. by annual
installments of 1000 each. The number of years by which debt will be cleared is
(a) 14.2 (b) 10 (c) 12 (d) 17

87. A person retires at 60 years receiving a pension of 14,400 a year paid in half yearly
installments for the rest of his life with his life expectation to be 13 years and interest
at 4% p.a. payable half yearly. What single sum is equivalent to his pension?
(a) 144000 (b) 144900 (c) 144600 (d) 144300

88. If discount rate is 7% p.a., how much would you pay to receive 500, growing at 5%
annually forever?
(a) 25000 (b) 250000 (c) 2500 (d) none

PAST YEARS QUESTION

89. The present value of an annuity of ` 3,000 for 15 years at 4.5% p.a. C.I. is:
[Given that (1.045)15 = 1.935282]
(a) ` 23, 809.67 (b) ` 32,218.67
(c) ` 32, 908.67 (d) ` None of these

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90. A machine can be purchased for `50,000. Machine will contribute `12,000 per year
for the next five years. Assume borrowing cost is 10% per annum. Determine whether
machine should be purchased or not:
(a) Should be purchased (b) Should not be purchased
(c) Can’t say about purchase (d) None of the above

91. How much amount is required to be invested every year so as to accumulate
`3,00,000 at the end of 10 years, if interest is compounded annually at 10%?
[Given (1.1)10 = 2.5937]
(a) ` 18,823.65 (b) ` 18,828.65
(c) ` 18,832.65 (d) ` 18,882.65

92. A company considering proposal of purchasing a machine either by, making full
payment of `4000 or by leasing it for four years at an annual rate of `1,250. Which
course of action is preferable, if the company can borrow money at 14% compounded
annually?
[Given: (1.14)4 = 1.68896]
(a) Leasing is preferable (b) Should be Purchased
(c) No difference (d) None of these

93. Vipul Purchases a car for `5,50,000. He gets a loan of `5,00,000 at 15% P.a. from a
bank and balance `50,000 he pays at the time of purchase. He has to pay the whole
amount of loan in 12 equal monthly instalments with interest starting from the end
of the first month. The money he has to pay at the end of every month is:
[Given (1.0125)12 = 1.16075452]
(a) ` 45,130.43 (b) ` 45,230.43 (c) ` 45,330.43 (d) ` None of these

94. A company establishes a sinking fund to provide for the payment of ` 2,00,000 debt
maturing in 20 years. Contributions to the fund are to be made at the end of every
year. Find the amount of each annual deposit if Interest is 5% per annum.
(a) ` 6,142 (b) ` 6,049 (c) ` 6,052 (d) ` 6,159

95. A company may obtain a machine either by leasing it for 5 years (useful life) at an
annual rent of `2,000 or by purchasing the machine for `8,100. If the company can
borrow money at 18% per annum, which alternative is preferable?
(a) Leasing (b) Purchasing (c) Can’t say (d) None of these

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96. A sinking fund is created for redeeming debentures worth `5 lacs at the end of 25
years. How much provision needs to be made out of profits each year provided
sinking fund investments can earn interest at 4% p.a?
(a) ` 12,006 (b) ` 12,040 (c) ` 12,039 (d) ` 12,035

97. Find the present value of an annuity of `1,000 payable at the end of each year for
10 years. If rate of interest is 6% compounding per annum (Given (1.06)-10 = 0.5584):
(a) ` 7,360 (b) ` 8,360 (c) ` 12,000 (d) None of these

98. The future value of an annuity of ` 5,000 is made annually for 8 years at interest
rate of 9% compounded annually. [Given (1.09)8 = 1.99256] is _____
(a) ` 55,142.22 (b) ` 65,142.22
(c) ` 65,532.22 (d) ` 57,425.22

99. How much amount is required to be invested every year as to accumulate ` 6,00,000
at the end of 10 years, if Interest is compounded annually at 10% rate of interest
[Given (1.1)10 = 2.59374].
(a) ` 37,467 (b) `37,476 (c) ` 37,647 (d) ` 37,674

100. The future value of an annuity of ` 1,500 made annually for five years at interest
rate 10% compounded annually is (Given that (1.1)5 =1.61051):
(a) ` 9,517.56 (b) ` 9,157.65
(c) ` 9,715.56 (d) ` 9,175.65

101. How much amount is required to be invested every year so as to accumulate

`3,00,000 at the end of 10 years, if interest is compounded annually at 10%?
(a) ` 18,823.65 (b) ` 18
(c) ` 18,828.65 (d) ` 18,882.65

102. The future value of an annuity of `1,000. Made annually for 5 years at the interest
of 14% compounded annually is: (Given (1.14)5 =1.92541):
(a) ` 5,610 (b) ` 6,610 (c) ` 6,160 (d) ` 5,160

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103. A person wants to lease out a machine costing ` 5,00,000 for a 10 year period. It
has fixed a rental of ` 51, 272 per annum payable annually starting from the end
of first year. Suppose rate of interest is 10% per annum compounded annually on
which money can be invested. To whom this agreement is favourable?
(a) Favour of lessee (b) Favour of lessor
(c) Not for both (d) Can’t be determined

104. Let a person invest a fixed sum at the end of each month in an account paying
interest 12% per year compounded monthly. If the future value of this annuity after
the 12th payment is ` 55,000 then the amount invested every month is?
(a) ` 4,837 (b) ` 4,637 (c) ` 4,337 (d) ` 3,337

105. Determine the present value of perpetuity of `50,000 per month @ rate of interest
12% p.a. is _____
(a) ` 45,00,000 (b) ` 50,00,000
(c) ` 55,00,000 (d) ` 60,00,000

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HOMEWORK SECTION

1. S.I on ` 3,500 for 3 years at 12% per annum is

(a) ` 1,200 (b) ` 1,260 (c) ` 2,260 (d) none of these

2. P = 5,000, R = 15, T = 4 ½ using I = PRT/100, I will be

(a) ` 3,375 (b) ` 3,300 (c) ` 3,735 (d) none of these

3. If P = 5,000, T = 1, I = ` 300, R will be

(a) 5% (b) 4% (c) 6% (d) none of these

4. If P = ` 4,500, A = ` 7,200, than Simple interest i.e. I will be

(a) ` 2,000 (b) ` 3,000 (c) ` 2,500 (d) ` 2,700

5. P = ` 12,000, A = ` 16,500, T = 2 ½ years. Rate percent per annum simple interest

will be
(a) 15% (b) 12% (c) 10% (d) none of these

6 P = ` 10,000, I = ` 2,500, R = 12 ½% SI. The number of years T will be

(a) 1 ½ years (b) 2 years (c) 3 years (d) none of these

7. P = ` 8,500, A = ` 10,200, R = 12 ½ % SI, t will be.

(a) 1 yr. 7 mth. (b) 2 yrs. (c) 1 ½ yr. (d) none of these

8. The sum required to earn a monthly interest of ` 1,200 at 18% per annum SI is
(a) ` 50,000 (b) ` 60,000
(c) ` 80,000 (d) none of these

9. A sum of money amount to ` 6,200 in 2 years and ` 7,400 in 3 years. The principal
and rate of interest are
(a) ` 3,800, 31.57% (b) ` 3,000, 20%
(c) ` 3,500, 15% (d) none of these

10. A sum of money doubles itself in 10 years. The number of years it would triple itself is
(a) 25 years. (b) 15 years. (c) 20 years (d) none of these

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11. If P = ` 1,000, R = 5% p.a, n = 4; What is Amount and C.I. is

(a) ` 1,215.50, ` 215.50 (b) ` 1,125, ` 125
(c) ` 2,115, ` 115 (d) none of these

12. ` 100 will become after 20 years at 5% p.a compound interest amount of
(a) ` 250 (b) ` 205 (c) ` 265.50 (d) none of these

13. The effective rate of interest corresponding to a nominal rate 3% p.a payable half
yearly is
(a) 3.2% p.a (b) 3.25% p.a (c) 3.0225% p.a (d) none of these

14. A machine is depreciated at the rate of 20% on reducing balance. The original cost
of the machine was ` 1,00,000 and its ultimate scrap value was ` 30,000. The
effective life of the machine is
(a) 4.5 years (appx.) (b) 5.4 years (appx.)
(c) 5 years (appx.) (d) none of these

15. If A = ` 1,000, n = 2 years, R = 6% p.a compound interest payable half-yearly, then

principal (P) is
(a) ` 888.48 (b) ` 885 (c) 800 (d) none of these

16. The population of a town increases every year by 2% of the population at the
beginning of that year. The number of years by which the total increase of population
be 40% is
(a) 7 years (b) 10 years (c) 17 years (app) (d) none of these

17. The difference between C.I and S.I on a certain sum of money invested for 3 years at
6% p.a is ` 110.16. The sum is
(a) ` 3,000 (b) ` 3,700 (c) ` 12,000 (d) ` 10,000

18. The useful life of a machine is estimated to be 10 years and cost ` 10,000. Rate of
depreciationis 10% p.a. The scrap value at the end of its life is
(a) ` 3,486.78 (b) ` 4,383 (c) ` 3,400 (d) none of these

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19. The effective rate of interest corresponding a nominal rate of 7% p.a convertible
quarterly is
(a) 7% (b) 7.5% (c) 5% (d) 7.18%

20. The C.I on ` 16000 for 1 ½ years at 10% p.a payable half -yearly is
(a) ` 2,222 (b) ` 2,522 (c) ` 2,500 (d) none of these

21. The C.I on ` 40000 at 10% p.a for 1 year when the interest is payable quarterly is
(a) ` 4,000 (b) ` 4,100 (c) ` 4,152.51 (d) none of these

22. The difference between the S.I and the C.I on ` 2,400 for 2 years at 5% p.a is
(a) ` 5 (b) ` 10 (c) ` 16 (d) ` 6

23. The annual birth and death rates per 1,000 are 39.4 and 19.4 respectively. The
number of years in which the population will be doubled assuming there is no
immigration or emigration is
(a) 35 years. (b) 30 years. (c) 25 years (d) none of these

24. The C.I on ` 4,000 for 6 months at 12% p.a payable quarterly is
(a) ` 243.60 (b) ` 240 (c) ` 243 (d) none of these

25. The present value of an annuity of ` 3000 for 15 years at 4.5% p.a CI is
(a) ` 23,809.41 (b) ` 32,218.63
(c) ` 32,908.41 (d) none of these

26. The amount of an annuity certain of ` 150 for 12 years at 3.5% p.a C.I is
(a) ` 2,190.28 (b) ` 1,290.28 (c) ` 2,180.28 (d) none of these

27. A loan of ` 10,000 is to be paid back in 30 equal instalments. The amount of each
installment to cover the principal and at 4% p.a CI is
(a) ` 587.87 (b) ` 587 (c) ` 578.30 (d) none of these

28. A = ` 1,200 n = 12 years i = 0.08, V = ?

Using the formula V= value of v will be
(a) ` 3,039 (b) ` 3,990 (c) ` 9930 (d) none of these

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29. a = ` 100 n = 10, i = 5% find the FV of annuity

Using the formula FV = a / {1 + i)n – 1}, FV is equal to
(a) ` 1,258 (b) ` 2,581 (c) ` 1,528 (d) none of these

30. If the amount of an annuity after 25 years at 5% p.a C.I is ` 50,000 the annuity will
be
(a) ` 1,406.90 (b) ` 1,047.62 (c) ` 1,146.90 (d) none of these

31. Given annuity of ` 100 amounts to ` 3137.12 at 4.5% p.a C. I. The number of years
will be
(a) 25 years (appx.) (b) 20 years (appx.)
(c) 22 years (d) none of these

32. A company borrows ` 10,000 on condition to repay it with compound interest at 5%

p.a by annual installments of ` 1000 each. The number of years by which the debt
will be clear is
(a) 14.2 years (b) 10 years (c) 12 years (d) none of these

33. Mr. X borrowed ` 5,120 at 12 ½ % p.a C.I. At the end of 3 yrs, the money was repaid
along with the interest accrued. The amount of interest paid by him is
(a) ` 2,100 (b) ` 2,170 (c) ` 2,000 (d) none of these

34. Mr. Paul borrows ` 20,000 on condition to repay it with C.I. at 5% p.a in annual
installments of ` 2000 each. The number of years for the debt to be paid off is
(a) 10 years (b) 12 years (c) 11 years (d) none of these

35. A person invests ` 500 at the end of each year with a bank which pays interest at
10% p. a C.I. annually. The amount standing to his credit one year after he has
made his yearly investment for the 12th time is.
(a) ` 11,761.36 (b) ` 10,000 (c) ` 12,000 (d) none of these

36. The present value of annuity of ` 5,000 per annum for 12 years at 4% p.a C.I.
annually is
(a) ` 46,000 (b) ` 46,850 (c) ` 15,000 (d) none of these

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37. A person desires to create a fund to be invested at 10% CI per annum to provide for
a prize of ` 300 every year. Using V = a/I find V and V will be
(a) ` 2,000 (b) ` 2,500 (c) ` 3,000 (d) none of these

38. A = ` 5,200, R = 5% p.a., T = 6 years, P will be

(a) ` 2,000 (b) ` 3,880 (c) ` 3,000 (d) none of these

39. If P = 1,000, n = 4 years., R = 5% p.a then C. I will be

(a) ` 215.50 (b) ` 210 (c) ` 220 (d) none of these

40. The time in which a sum of money will be double at 5% p.a C.I is
(a) ` 10 years (b) 12 years (c) 14.2 years (d) none of these

41. If A = ` 10,000, n = 18yrs., R = 4% p.a C.I, P will be

(a) ` 4,000 (b) ` 4,900 (c) ` 4,500 (d) none of these

42. The time by which a sum of money would treble it self at 8% p. a C. I is

(a) 14.28 years (b) 14 years (c) 12 years (d) none of these

43. The present value of an annuity of ` 80 a years for 20 years at 5% p.a is

(a) ` 997 (appx.) (b) ` 900 (c) ` 1,000 (d) none of these

44. A person bought a house paying ` 20,000 cash down and ` 4,000 at the end of each
year for 25 yrs. at 5% p.a. C.I. The cash down price is
(a) ` 75,000 (b) ` 76,000 (c) ` 76,392 (d) none of these.

45. A man purchased a house valued at ` 3,00,000. He paid ` 2,00,000 at the time of
purchase and agreed to pay the balance with interest at 12% per annum compounded
half yearly in 20 equal half yearly instalments. If the first instalment is paid after
six months from the date of purchase then the amount of each instalment is
[Given log 10.6 = 1.0253 and log 31.19 = 1.494]
(a) ` 8,719.66 (b) ` 8,769.21 (c) ` 7,893.13 (d) none of these.

46. The difference between compound and simple interest at 5% per annum for 4 years
on ` 20,000 is ` ________
(a) 250 (b) 277 (c) 300 (d) 310

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47. The compound interest on half-yearly rests on ` 10,000 the rate for the first and
second years being 6% and for the third year 9% p.a. is `.____________.
(a) 2,200 (b) 2,287 (c) 2,285 (d) None

48. The present value of ` 10,000 due in 2 years at 5% p.a. compound interest when the
interest is paid on yearly basis is ` ________.
(a) 9,070 (b) 9,000 (c) 9,061 (d) None

49. The present value of ` 10,000 due in 2 years at 5% p.a. compound interest when the
interest is paid on half-yearly basis is ` ________.
(a) 9,070 (b) 9,069 (c) 9,059.50 (d) None

50. Johnson left ` 1,00,000 with the direction that it should be divided in such a way
that his minor sons Tom, Dick and Harry aged 9, 12 and 15 years should each
receive equally after attaining the age 25 years. The rate of interest being 3.5%,
how much each son receive after getting 25 years old?
(a) 50,000 (b) 51,994 (c) 52,000 (d) None

51. In how many years will a sum of money double at 5% p.a. compound interest?
(a) 15 years 3 months (b) 14 years 2 months
(c) 14 years 3 months (d) 15 years 2 months

52. In how many years a sum of money trebles at 5% p.a. compound interest payable
on halfyearly basis?
(a) 18 years 7 months (b) 18 years 6 months
(c) 18 years 8 months (d) 22 years 3 months

53. A machine depreciates at 10% of its value at the beginning of a year. The cost and
scrap value realized at the time of sale being ` 23,240 and ` 9,000 respectively. For
how many years the machine was put to use?
(a) 7 years (b) 8 years (c) 9 years (d) 10 years

54. A machine worth ` 4,90,740 is depreciated at 15% on its opening value each year.
When its value would reduce to ` 2,00,000?
(a) 4 years 6 months (b) 4 years 7 months
(c) 4 years 5 months (d) 5 years 7 months approximately

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55. A machine worth ` 4,90,740 is depreciated at 15% of its opening value each year.
When its value would reduce by 90%?
(a) 11 years 6 months (b) 11 years 7 months
(c) 11 years 8 months (d) 14 years 2 months approximately

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HOMEWORK SOLUTION

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SELF ASSESSMENT TEST 7

ANNUITIES
25 Question, 25 Marks

1. Find the amount of an immediate annuity of Rs. 100 in 10 years allowing compound
interest at 5%, given (1.05)10 = 1.6289.
a) Rs. 1527.80 b) Rs. 1257.80
c) Rs. 1357.90 d) None of the above

2. Find the present value of an annuity certain of Rs. 300 for 5 years reckoning
compound interest at 4% per annum. Given (1.04)5 = 1.2167
a) Rs. 1335.78 b) Rs. 1353.87
c) Rs. 1533.98 d) None of the above

3. Gargi borrows Rs. 20000 at 4% compound interest and agrees to pay both the
principal and the interest in 10 equal annual instalments at the end of each year.
Find the amount of these in-stalments. Given (1.04)10 = 1.4802.
a) Rs. 2470 b) Rs. 2570 c) Rs. 2740 d) Rs. 2760

4. Find the amount of an annuity of Rs. 50 payable quarterly for 15 years at 5%,
compounded quarterly. Given (1.0125)60 = 2.1028
a) Rs. 4422 b) Rs. 4411 c) Rs. 5544 d) Rs. 4433

5. Find the present value of an annuity of Rs. 50 payable quarterly for 15 years at 5%,
compound-ed quarterly. Given (1.0125)60 = 2.1028
a) Rs. 2000 b) Rs. 2098 c) Rs. 2108 d) Rs. 2100

6. Find the value of perpetuity of Rs. 105 a year at 5.25% per annum.
a) Rs. 2000 b) Rs. 2098 c) Rs. 2108 d) Rs. 2100

7. A wagon is purchased on instalment basis, such that Rs. 5000 is to be paid on the
signing of the contract and four yearly instalment of Rs. 3000 each payable at the
end of the first, second, third and fourth years. If interest is charged at 5% p.a.,
what would be the cash down price? Given (1.05)-4 = 0.82270
a) Rs. 16358 b) Rs. 15638 c) Rs. 10638 d) Rs. 14500

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8. A government constructed housing flat costs Rs. 136000; 40% is to be paid at the
time of possession and the balance, reckoning compound interest of 9% p.a. is to
be paid in 12 equal annual instalments. Find the amount of each such instalment.
Given (1.09)-12 = 0.3558
a) Rs. 11000 b) Rs. 12000 c) Rs. 11400 d) Rs. 12400

9. What sum will buy an annuity of Rs. 1000 payable half-yearly for 5 years, the rate
of interest being 8% p.a. compounded half-yearly? Given (1.04)-10 = 0.6756
a) Rs. 8000 b) Rs. 9000 c) Rs. 9110 d) Rs. 8110

10. Dipti borrowed Rs. 40000 at 6% compound interest promising to repay Rs. 9000 at the
end of each of the first four years and to pay the balance at the end of the fifth year.
Ascertain how much she would pay as the final instalment. Given (1.06)-4 = 0.79206
a) Rs. 8809 b) Rs. 11789 c) Rs. 12897 d) Rs. 10589

11. The present vale and amount of an annuity certain of Rs. 180 at a fixed rate per cent
p.a. com-pound are Rs. 2000 and Rs. 3000 respectively. Find the rate of interest.
a) 4% b) 3.5% c) 5% d) 3%

12. A man retires at the age of 60 years and his employer gives him a pension of Rs.
3600 a year paid in half-yearly instalments for the rest of his life. If the expectation
of his life is taken to be 10 years and interest is 6% per annum payable half-yearly,
determine the present value of the pension. Given (1.03)-20 = 0.55362
a) Rs. 26,783 b) Rs. 28,768 c) Rs. 26,893 d) Rs. 28,763

13. A freehold estate was worth Rs. 50,000. If the annual rent of the property be Rs.
2,000, find the rate per cent p.a.
a) 3% b) 3.5% c) 4% d) 5%

14. A machine costs a company Rs. 52000 and its effective life is estimated to be 25
years. A sinking fund is created for replacing the machine by a new model at the
end of its life-time, when its scrap realizes a sum of Rs. 2500 only. The price for the
new model is estimated to be 25% higher than the price of the present one. Find
what amount should be set aside every year out of profits for the sinking fund, if it
accumulates at 3.5% p.a. compound. Given (1.035)25 = 2.3659
a) Rs. 1590 b) Rs. 1650 c) Rs. 1602 d) Rs. 1592

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15. A man decides to deposit Rs. 10000 at the end of each year in a bank which pays
10% per annum compound interest. If the instalments are allowed to accumulate,
what will be total accumulation at the end of 9 years? Given (1.1)9 = 2.2583
a) Rs. 124000 b) Rs. 125000 c) Rs. 125830 d) Rs. 124930

16. The annual rent of a perpetual annuity is Rs. 4000. Find its value, the interest being
compounded at 8% p.a.
a) Rs. 40000 b) Rs. 45000 c) Rs. 50000 d) None of the above

17. The value and annual rent of perpetuity are Rs. 12500 and Rs. 1000 respectively.
Find the rate of compound interest.
a) 7% b) 8% c) 10% d) None of the above

18. Find the value of a deferred perpetuity of Rs. 500 p.a. to commence 10 years hence
at 6% p.a. compound interest. Given (1.06)10 = 1.791
a) Rs. 4653 b) Rs. 4563 c) Rs. 4356 d) Rs. 4365

19. A loan of Rs. 10,000 is to be repaid in 30 equal annual instalments of Rs. X. Find X,
if the CI charged is at the rate of 4% p.a. (Annuity is an annuity immediate). Given
(1.04)30 = 3.2434
a) Rs. 878.80 b) Rs. 758.40 c) Rs. 578.40 d) Rs. 598.80

20. A man buys a house for Rs. 60,000 on condition that he will pay Rs. 30000 cash
down and the balance in 10 equal annual instalments, the first to be paid one year
after the date of purchase. Calculate the amount of each instalment, compound
interest being computed at the rate of 5% p.a. Given (1.05)-10 = 0.6139
a) Rs. 5883 b) Rs. 3885 c) Rs. 8583 d) Rs. 3588

21. The annual subscription for the membership of a club is Rs. 25 and a person may
become a life-member by paying Rs. 1000 in a lump sum. Find the rate per cent per
annum.
a) 2% b) 3% c) 2.5% d) 3.5%

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22. An overdraft of Rs. 50,000 is to be paid back in equal instalments over a period of
20 years. Find the value of the instalment, if interest is compounded annually at
14% per annum. Given (1.14)20 = 13.74349
a) Rs. 7549 b) Rs. 7561 c) Rs. 7571 d) Rs. 7539

23. What is the value of an annuity at the end of 5 years, if Rs. 100 per month is
deposited into an account earning interest 9% per year compounded monthly?
Given log10075 = 4.003245055 and antilog 4.1947033 = 15656.81067
a) Rs. 7542 b) Rs. 7892 c) Rs. 7598 d) Rs. 7498

24. A man borrows Rs. 20,000 at interest rate 4% per annum compounded annually and
agrees to pay both the principal and the interest in 10 equal annual instalments at
the end of each year. Find the amount of these instalments. Given log104 = 2.0170
and log6761 = 3.8300
a) Rs. 2400 b) Rs. 2470 c) Rs. 2489 d) Rs. 2459

25. Rs. 12,000 is invested at the end of each month in an account paying interest 6% per
year compounded monthly. What is the amount of this annuity after 10th payment?
Given (1.005)10 = 1.0511
a) Rs. 122000 b) Rs. 120680 c) Rs. 122980 d) Rs. 122640

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EXPLANATORY
ANSWERS

1. A = 100/0.05[(1.05)10 – 1] = 2000(1.6289 – 1) = 1257.80, Option B

2. PV = 300/0.04[1-(1.04)-5] = 7500[1 – 1/1.2167] = 1335.78. Option A

3. 20000 = P/0.04[1 – (1.04)-10]

800 = P[1 – 1/1.4802]
P = (800 * 1.4802)/0.4802 = 2470
Option A

4. Amount = 50/0.0125[(1.0125)60 – 1] = 4000(1.1028) = 4411. Option B

5. PV = 50/0.0125[1 – (1.0125)-60] = 4000(1.1028/2.1028) = 2098. Option B

6. Perpetuity PV = 105/5.25% = 2000. Option A

7. PV of instalment = 3000/0.05[1 – 0.82270] = 10638

Cash down price = 5000 + 10638 = 15638. Option B

8. Loan amount = 136000 * .60 = 81600

81600 = P/0.09 [1 – 0.3558]
7344 = P(0.6442)
P = 11400. Option C

9. PV = 1000/0.04[1 – 0.6756] = 25000(0.3244) = 8110. Option D

10. PV of 4 instalments = 9000/0.06[1 – 0.79206] = 31191

PV of loan amount remaining to be paid = 40000 – 31191 = 8809
FV of Rs. 8809 payable after 5 years = 8809(1.06)5 = 11789
Option B

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11. 2000 = 180/r[1 – (1+r)-n] = 180/r[(1+r)n – 1]/(1+r)n = 3000/(1+r)n

3000 = 180/r[(1+r)n – 1]
3/2 = (1+r)n
3000 = 180/r[3/2 – 1]
r = 180/3000[1/2] = 0.03
Interest rate = 3%
Option D

12. PV = 1800/0.03[1 – (1.03)-20] = 60000[1 – 0.55362] = 26783. Option A

13. R/100 = 2000/50000 = 0.04. R = 4%. Option C

14. Amount required = 52000 * 1.25 – 2500 = 62500

62500 = A/.035[(1.035)25 – 1] = A(39.0257)
A = 62500/39.0257 = 1602. Option C

15. FV = 10000/0.10 [(1.1)9 – 1] = 100000[2.2583 – 1] = 125830. Option C

16. Value = 4000/0.08 = 50000. Option C

17. R/100 = 1000/12500 = 0.08. R = 8%. Option B

18. Value = 500/0.06 = 8333

PV of Value = 8333/(1.06)10 = 8333/1.791 = 4653. Option A

19. 10000 = X/0.04 [1 – 1/3.2434] = X(17.292)

X = 10000/17.292 = 578.40. Option C

20. 30000 = X/0.05[1 – 0.6139] = X(7.722)

X = 30000/7.722 = 3885. Option B

21. R/100 = 25/1000 = 0.025. R = 2.5%. Option C

22. 50000 = X/0.14[1 – 1/13.74349] = X(6.6231)

X = 50000/6.6231 = 7549. Option A

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23. Amount = 100/0.0075[(1.0075)60 – 1]

X = (1.0075)60
LogX = 60 log(1.0075) = 60[0.003245055] = 0.1947033 = Log 1.565681067
X = 1.565681067
Amount = 13333.33(1.565681067 – 1) = 7542. Option A

24. 20000 = P/0.04[1 – (1.04)-10]

Let X = (1.04)10
Log X = 10 log(1.04) = 10(0.0170) = 0.170 = 4 – 3.83 = log 10000 – log 6761 = log
1.4791
X = 1.4791
20000 = P/0.04[1 – 1/1.4791] = P(8.098)
P = 20000/8.098 = 2470
Option B

25. Amount = 12000/0.005[(1.005)10 – 1] = 2400000(0.0511) = 122640. Option D

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SELF ASSESSMENT TEST 8

INTEREST
25 Question, 25 Marks

1. Mahesh lent Rs. 100000, partly at 12% and partly at 10% simple interest. After
three years he got Rs. 31500 as total simple interest. How much did he lend at the
12%?
a) 25000 b) 75000 c) 50000 d) 40000

2. At what rate will a sum of money Rs. 205000, becomes Rs. 410000 with simple
interest in 20 years?
a) 5% b) 6.67% c) 5.5% d) 7.14%

3. A sum of money amounts to Rs. 44700 in 14 years at 8.33% simple interest. When
will it double itself at the same rate?
a) 16 years b) 12 years c) 11 years d) 17 years

4. A sum of Rs. 57000 is lent out in two parts A and B in such a way that interest on
A @ 8% per annum simple interest for 5 years is equal to that on B at 0.5% per
annum sim-ple interest for 15 years. Find the value of A.
a) 9000 b) 6000 c) 48000 d) 45000

5. A sum of money A becomes 3A in 9 yrs at R% per annum simple interest. In how

many years will it be 5A at R% per annum simple interest?
a) 16 years b) 18 years c) 20 years d) 15 years

6. In what time will Rs. 4,500 amount to 22,500 at 4% per annum simple interest?
a) 50 b) 60 c) 110 d) 100

7. Mr. M takes a loan of Rs. 525000 at 4% p.a. Simple Interest from Mr. J. He pays Mr.
J Rs. 250000 at the end of 1st year. How much should he pay at the end of the 2nd
year in order to clear his dues?
a) 300000 b) 300800 c) 307840 d) 370480

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8. A person bought a robot under the following scheme: Down payment of Rs. 150,000
and the rest amount at 8% per annum for 2 years. In this way, he paid Rs. 289,200
in total. Find the actual price of the robot. (Assume simple interest).
a) 270000 b) 300000 c) 280000 d) 275000

9. Manohar Bhaiya borrows Rs. 140,000 at simple interest from the village co-
operative society bank. At the end of 3 years, he again borrows Rs. 60,000 and
closes his account after paying Rs. 92,300 as interest after 8 years from the time he
made the first bor-rowing. What is the simple interest rate of interest charged by
the bank?
a) 6.5% b) 5.5% c) 5% d) 7%

10. At R% per annum simple interest, simple interest on Rs. X for 20 years is equal to
4/9 th of its amount for that period. Find R.
a) 4% b) 5% c) 4.5% d) 6.5%

11. Rs. X lent out at compound interest amounts to Rs. 484000 in 2 years at 10% p.a.
Find X.
a) 400000 b) 410000 c) 390000 d) 380000

12. A sum of money doubles itself in 5 years @ R% per annum compounded annually. In
how many years will it become four times at the same compound rate on interest?
a) 10 b) 8 c) 12 d) 17

13. Rs. X doubles itself and becomes Rs. 2X at a certain rate of compound interest in 3
years. In how many years will the ratio of the principal to the compound interest be
1:3?
a) 6 b) 5 c) 8 d) 7.5

14. Rs. 12500 placed at compound interest becomes Rs. 250000 in 3 years @ R% per
annum compound interest? In how many years will it amount becomes 1000000?
a) 9 years b) 10 years c) 11 years d) 7 years

15. Rs. M grows up to Rs. 80000 in 2 yrs. and up to Rs. 85000 in 3 yrs @ R% per annum
compound interest. Find the value of R.
a) 6.25% b) 6% c) 6.75% d) 5.5%

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16. An amount of money grows upto Rs. 86400 in 2 years and upto Rs. 103680 in 3
years on compound interest. What is the sum?
a) Rs. 51000 b) Rs. 61000 c) Rs. 58000 d) Rs. 60000

17. The difference between Compound interest and simple interest on a certain sum of
money is Rs. 400 for first two years and Rs. 1220 for first three years. Find the sum,
if the rate is same in both the cases.
a) 6400 b) 8000 c) 12000 d) 9400

18. The Compound Interest @ R% per annum on a certain sum of money Rs. X for 2 yrs.
is Rs. 357 and the Simple Interest on the same sum of money Rs. X at the same rate
of in-terest is Rs. 350. What is the value of R?
a) 4% b) 5% c) 4.5% d) 5.5%

19. The value of a residential flat constructed at a cost of Rs. 15,00,000 is depreciating
at the rate of 9% per annum. Find its value after two years of construction.
a) 12,42,150 b) 12,50,000 c) 12,75,850 d) 12,95,540

20. A money lender borrows a sum from market at 3% per annum simple interest and
lent it out to another person at 6% per annum compounded half-yearly. If after
one year, he gets a profit of Rs. 618, then find out the sum borrowed by the money
lender.
a) Rs. 25,000 b) Rs. 20,000
c) Rs. 18,000 d) Can’t be determined

21. The simple interest on a certain sum of money for 2 years at 12% per annum is Rs.
3120. What would be the compound interest at the same rate and for the same
time?
a) Rs. 3507.80 b) Rs. 3407.20
c) Rs. 3207.20 d) Rs. 3307.20

22. What would be the compound interest on Rs. 10000 for three years, if the rate of
inter-est is 5% for the first year, 6% for the second year and 7% for the third year?
a) Rs. 1900.10 b) Rs. 1919.10
c) Rs. 1909.10 d) Rs. 1809.10

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23. Rs. 4000 becomes Rs. 5000 in 4 years at a certain rate of compound interest. What
will be the sum at the end of 12 years?
a) Rs. 7812.50 b) Rs. 7612.50
c) Rs. 7712.50 d) Rs. 7512.50

24. Simple interest on a sum for 3 years at any rate of interest is Rs. 225 while compound
interest on the same sum at the same rate for 2 years is Rs. 153. Find the sum and
rate percent.
a) Rs. 1875, 4% b) Rs. 1875, 5%
c) Rs. 1785, 4% d) Rs. 1785, 5%

25. A man borrows Rs. 6000 at 10% compound rate of interest. At the end of each year
he pays back Rs. 2000. How much amount should be pay at the end of third year to
clear all his dues?
a) Rs. 3636 b) Rs. 3663 c) Rs. 3366 d) None of the above

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EXPLANATORY
ANSWERS

1. X * 0.12 * 3 + (100000 – X) * 0.10 * 3 = 31500

0.36X + 30000 – 0.30X = 31500
0.06X = 1500
X = 25000; Option A

2. 410000/205000 = 2; Doubled; Rate = 100/20 = 5%. Option A

3. Time = 100/8.33 = 12 years. Option B

4. A * 0.08 * 5 = (57000 – A) * 0.005 * 15

0.4A = 4275 – 0.075A
A = 4275 / 0.475 = 9000; Option A

5. Earnings - 2A in 9 years, 4A in 18 years. Option B

6. 22500 – 4500 = 18000 = 4500 * 0.04 * T

T = 18000/180 = 100 years; Option D

7. 525000 * 1.04 = 546000 – 250000 = 296000 x 1.04 = 307840. Option C

8. 150000 + X(1.16) = 289200

X = 120000; Actual price = 150000 + 120000 = 270000; Option A

9. 140000 * R/100 * 3 + 200000 * R/100 * 5 = 92300

4200R + 10000R = 92300
R = 6.5%; Option A

10. X * R/100 * 20 = 4X (1 + 20R/100)/9

9R/5 = 4 + 4R/5
R = 4, Option A

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11. 484000 = X (1.1)2

X = 484000/1.21 = 400000; Option A

12. Doubles = 5 years, Four times = 5 * 2 = 10 years. Option A

13. Double 3 years

1:3 means Sum now becomes 4 times.
Four times 3*2 = 6 years; Option A

14. Double 3 years

Eight times = 3*3 = 9 years; Option A

15. 5000 = 80000 * R/100

R = 5000/800 = 6.25%; Option A

16. (103680 – 86400) = 17280 = Interest on 86400 for 1 years

R = 17280 / 86400 * 100 = 20%
P = 86400 / (1.2)2 = 60000
Option D

17. PII = 400

PII (I/100 + 3) = 1220
I/100 = 0.05
I = 5%
P (25/100 ) (25/100) =400
P = 400 * 4 * 4 = 6400
Option A

18. X * R/100 * R/100 = 7

2X * R/100 = 350
XR/100 = 175
175 * R/100 = 7
R=4
Option A

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19. Value = 1500000 (1 – 0.09)2 = 1242150. Option A

20. 3% pa CI is equivalent to (1.03)2 – 1 = 6.09% pa SI

Profit = 3.09% = 618
100% = Sum borrowed = 618/3.09% = 20000. Option B

21. P = 3120 / 24% = 13000

CI = 13000 [ (1.12)2 – 1] = 13000 * 0.2544 = 3307.20.
Option D

22. CI = 10000 [ (1.05)(1.06)(1.07) – 1] = 10000 * 0.19091 = 1909.10. Option C

23. In 4 years amount increases by 1000/4000 * 100 = 25%

In next 4 years 5000 shall become 5000 * 1.25 = 6250
In next 4 years 6250 shall become 6250 * 1.25 = 7812.50
Option A

24. Simple interest for 1 year = 225/3 = 75

Thus CI for 2 years = 75 + 75 + 75*R% = 153
75 * R/100 = 3
R = 300/75 = 4%
P = 225/12% = 1875; Option A

25. Year 1 – 6000 * 1.10 = 6600 – 2000 = 4600

Year 2 – 4600 * 1.1 = 5060 – 2000 = 3060
Year 3 – 3060 * 1.1 = 3366
Option C

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