COMPOUND INTREST EXAMPLE QUESTIONS

COMPOUND INTREST EXAMPLE QUESTIONS:

1) What total amount will Ravali get in 2 years. If she invests Rs.5000 to obtain compound interest at the rate of 5% per annum?

sol: Principal = 5000
---- Rate = 5%
     time (n) = 2 years
     Amount = principal*( 1+ (rate / 100))^n
            = 5000 * (1+ (5/100))^2
            = 5000 * ((100+5) / 100)^2
            = 5000 * (105 / 100)^2
            = 5000 * (21 / 20)^2
            = (5000* 21 * 21) / (20*20)
            = (25 * 21 * 21)/2
            = Rs.5512.50

2) Find the compound interest on Rs.10000 in 2 years at 4% per annum, the interest being compounded half yearly?
sol: principal = Rs.10000
---  rate = 2% per half year
     time = 2 years
     2 years = 4 half years
     amount = principal*[1+ (rate /(2* 100))]^2n
            = [10000 * (1+ ((4/2) /100)^4]
            = [10000 * (1+ (2/100))^4]
            = [10000 * (51/50)^4]
            = [(10000*51*51*51*51) / (50*50*50*50)]
            = Rs.10824.32
     compound interest = Amount - Principal
                = Rs. (10824.32 - 10000)
                       = Rs. 824.32

3) Find the compound interest on Rs.16000 at 20% per annum for 9 months. Find compounded quarterly?
sol: principal = Rs.16000
---- time = 9months
     9 months = 3 quarters
     Amount = [16000*(1+ ((20/5)/ 100)^3]
            = [16000 *(1+ (4/100)^3]
            = [(16000 * 21*21*21*21) / (20*20*20*20)]
            = Rs. 18522
    Compound interest = Rs. (18522 - 16000)
                      = Rs. 2522

4)Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
 sol: Principal = Rs.8000
 ---   A = 8000(21/20)3
        = 9261
      compound interest = 9261 - 8000
                  = 1261

5)Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?

Explanation:

9261 = 8000(21/20)^N

(21/20)^3 = (21/20)^N => N = 3

6) At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
Explanation:
prinncipal = 20000

A = 20000(11/10)3

    = 26620

compound interest = 26620 - 20000
                  = 6620

7)The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?

Explanation:

P = (184*10^6) / [6 2/3 * 6 2/3 *(300*6 2/3)]

P = 13500

8)A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
Explanation:

P(11/10)^4 - P(6/5)^2 = 482

P = 2000

9)Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
Explanation:

P = 15(100/10)2 => P = 1500

10)What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
Explanation:

8820 ---- 441

100 ---- ? => 5%

 x *105/100 * 105/100 = 8820

 x*1.1025=8820

 x=8820/1.1025 => 8000

11) Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Explanation:

A = 8000(21/20)^3 = 9261

12) Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
Explanation:

64000* 9/8 * 9/8 = 81000

13)Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Explanation:

1250 = D(100/4)^2

      D = 2

14) In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
Explanation:

x*110/100 * 90/100 = 7920

 X*0.99=7920

 X=7920/0.99

=> 8000

15) What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
Explanation:

A= P{1 + R/100}^n
 => 8000{1 + 10/100}^2  = Rs.9680

16) A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
A.0 Rs.2520 B. Rs.3120 C. Rs.3320 D. Rs.2760 E. None of these

Answer & Explanation
Answer: Option B

Explanation:

Let A be the amount received at the end of the three years.

A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120

17) A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
A. Rs.500 B. Rs.250 C. Rs.5012.50 D. Rs.5062.50 E. None of these.

Answer & Explanation
Answer: Option E

Explanation:

Let the principal be Rs.P

S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]^2 - 1} = 2500{ 21^2 - 20^2 /20^2}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25

18) The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
A. Rs.20043.94 B. Rs.18654.81 C. Rs.20264.46 D. Rs.19612.41 E. None of these

Answer & Explanation
Answer: Option A

Explanation:

Let the rate of interest be R% p.a.

(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]^3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.

19)A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
A. Rs.7500 B. Rs.7000 C. Rs.8000 D. Rs.6500 E. None of these

Answer & Explanation
Answer: Option A

Explanation:

P = (d * 100^2) / R^2

=> (48 * 100 * 100) / 8 * 8 = Rs.7500

20) The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum.
A. Rs.18000 B. Rs.17000 C. Rs.18500 D. Rs.17500 E. None of these.

Answer & Explanation
Answer: Option B

Explanation:

The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year

So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000

21)What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?
A. Rs.140 B. Rs.120 C. Rs.130 D. Rs.110 E. None of these.

Answer & Explanation
Answer: Option B

Explanation:

When compounded annually, interest

= 12000[1 + 20/100]^1 - 12000 = Rs.2400
When compounded semi-annually, interest
 = 12000[1 + 10/100]^2 - 12000 = Rs.2520
Required difference = 2520 - 2400 = Rs.120

22)The simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest.
A. Rs.3502.80 B. Rs.3052.40 C. Rs.3054.8 D. Rs.3052.80 E. None of these

Answer & Explanation
Answer: Option D

Explanation:

R = 100 I / PT 

=> R = (100 * 7200)/ (12000 * 5) = 12%
CI = P{ [1 + R /100]^n - 1}
= 12000 { [ 1 + 12 / 100]^2 - 1} = Rs.3052.80

23) Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
A. Rs.21.60 B. Rs.24.00 C. Rs.25.20 D. Rs.27.80 E. None of these

Answer & Explanation
Answer: Option A

Explanation:

Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000

He lend the same amount for C.I at 6% p.a. for two years.
 => Siddharth's income = C.I - S.I
= p[1 + r/ 100]^n - p - pnr/100
= p{ [1 + r/ 100]^2 - 1 - nr/100
= 6,000{ [1 + 6/100]^2 - 1 - 12/100}
= 6,000 {(1.06)^2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 = Rs.21.60

24) What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?
A. Rs. 9000.30 B. Rs. 9720 C. Rs. 10123.20 D. Rs. 10483.20

Answer & Explanation
Answer: Option C

Explanation:

Amount = [25000 * (1 + 12/100)^3]

= 25000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (35123.20 - 25000) = Rs. 10123.20

25)A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?
A. Rs. 565.25 B. Rs. 635 C. Rs. 662.02 D. Rs. 666.50
 
Answer & Explanation
Answer: Option C

Explanation:

Amount = [200(1 + 5/100)^3 + 200(1 + 5/100)^2 + 200(1 + 5/100)]

= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02

26) Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
A. Rs. 16,500B. Rs. 16,525.50C. Rs. 16,537.50D. Rs. 18,150

Answer & Explanation
Answer: Option C

Explanation:

P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year

Amount = [15000 * (1 + 5/100)^2]
= (15000 * 21/20 * 21/20) = Rs. 16537.50

27)What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
A. Rs. 2.04B. Rs. 3.06C. Rs. 4.80D. Rs. 8.30

Answer & Explanation
Answer: Option A

Explanation:

C.I. when interest is compounded yearly

= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 5000 * 26/25 * 51/50 = Rs. 5304
C.I. when interest is compounded half-yearly
= [5000 * (1 + 2/100)^2]
= (5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04 Difference = (5306.04 - 5304)
= Rs. 2.04

28) Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
A. Rs. 1851B. Rs. 1941C. Rs. 1951D. Rs. 1961

Answer & Explanation
Answer: Option C

Explanation:

P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.

Amount = [15625 * (1 + 4/100)^3]
= (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.

29) What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
A. Rs. 31B. Rs. 32.10C. Rs. 40.40D. Rs. 64.10

Answer & Explanation
Answer: Option D

Explanation:

S.I. = (1000 * 10 * 4)/100 = Rs. 400

C.I. = [1000 * (1 + 10/100)^4 - 1000] = Rs. 464.10 Difference = (464.10 - 400)
= Rs. 64.10

30) The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
A. 2B. 2 1/2C. 3D. 4

Answer & Explanation
Answer: Option A

Explanation:

Amount = (30000 + 4347) = Rs. 34347

Let the time be n years. Then,
30000(1 + 7/100)^n = 34347
= (107/100)^n = 34347/30000 = (107/100)^2
n = 2 years.

31)If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
A. Rs. 400B. Rs. 450C. Rs. 460D. Rs. 480

Answer & Explanation
Answer: Option D

Explanation:

Let the sum be Rs. P. Then,

[P(1 + 25/(2 * 100))^2 - P] = 510
P[(9/8)^2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480

32) The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
A. Rs. 1550B. Rs. 1650C. Rs. 1750D. Rs. 2000

Answer & Explanation
Answer: Option C

Explanation:

C.I. = [4000 * (1 + 10/100)^2 - 4000]

= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs. 1750

33) There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
A. Rs. 2160B. Rs. 3120C. Rs. 3972D. Rs. 6240

Answer & Explanation
Answer: Option C

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)^3 - 1}]
= 12000 * 331/1000 = Rs. 3972

34) The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?
A. 625B. 630C. 640D. 650

Answer & Explanation
Answer: Option A

Explanation:

Let the sum be Rs. x. Then,

[x (1 + 4/100)^2 - x] = (676/625 x - x) = 51/625 x
S.I. = (x * 4 * 2)/100 = 2x/25
51x/625 - 2x/25 = 1 or x = 625.

35) The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
A. 6.06%B. 6.07%C. 6.08%D. 6.09%

Answer & Explanation
Answer: Option D

Explanation:

Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)^2]
 = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09%

36)A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?
A. 7 yearsB. 10 yearsC. 15 yearsD. 20 years

Answer & Explanation
Answer: Option C

Explanation:

P(1 + R/100)^5 = 2P => (1 + R/100)^5 = 2

Let P(1 + R/100)^n = 8P
=> (1 + R/100)^n = 8 = 2^3 = {(1 + R/100)^5}^3
=> (1 + R/100)^n = (1 + R/100)^15 => n = 15 Required time = 15 years.

37) What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?
A. Rs. 550B. Rs. 551.25C. Rs. 560D. Rs. 560.75

Answer & Explanation
Answer: Option B

Explanation:

Let each installment be Rs. x. Then,

x/(1 + 5/100) + x/(1 + 5/100)^2 = 1025
820x + 1025 * 441
x = 551.25
So, value of each installment = Rs. 551.25

38)The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
A. 8B. 10C. 12D. Cannot be determined

Answer & Explanation
Answer: Option A

Explanation:

[15000 * (1 + R/100)^2 - 15000] - (15000 * R * 2)/100 = 96

15000[(1 + R/100)^2 - 1 - 2R/100] = 96
15000[(100 + R)^2 - 10000 - 200R]/10000 = 96
R^2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%

39) If Rs. 7500 are borrowed at C. I at the rate of 4 % per annum then after 2 years, the amount to be paid is?
A. Rs. 8082B. Rs. 7800C. Rs. 8100D. Rs. 8112

Answer & Explanation
Answer: Option D

Explanation:

Amount = Rs. [7500 (1 +4/100)2]


 = Rs. [7500 × 26/25 × 26/25] = Rs.8112

40)  Rs. 800 at 5 % Per annum compound interest will amount to Rs. 882 in?
A. 1 YearB. 2 yearsC. 3 YearsD. 4 Years

Answer & Explanation
Answer: Option B

Explanation:

Time be t years 882 = 800 (1 +5/100)^t


=> 882/800 =(21/20)^t

 (21/20)^2 = (21/20)^t

=> t = 2 Therefore,

Time = 2 years

41) The difference between the compound interest and the simple interest on a certain sum at 5 % per annum for 2 years is Rs. 1.50. The sum is?
A. Rs.600B. Rs.500C. Rs.400D. Rs.300

Answer & Explanation
Answer: Option A

Explanation:

Sum be Rs.100


S.I = Rs.(1000/100) =Rs.10


C.I = Rs.[{100 × (1 +5/100)^2} - 100] =Rs.41/4

Difference C.I amd S. I = Rs.(41/4 - 10) =Rs.25

25 : 1.50 :: 100 : x

Therefore x = ((1.50 ×100)/25) = Rs.600

42)The difference between compound interest and simple interest on Rs 8000 at 5% P.a for 3 years is
A. Rs 50B. Rs 60C. Rs 61D. Rs 600

Answer & Explanation
Answer: Option C

Explanation:

S.I = Rs(8000 × 5/100 ×3) = Rs 1200


C.I = Rs [8000 × (1+5/100)^3- 8000

= Rs [(8000 × 21/20×21/20×21/20)-8000]

=Rs (9261-8000)=Rs 1261

 (c.I)-(S.I) = Rs (1261 – 1200) = Rs61.

43)What will be the compound interest on Rs 25000 after 3 years at 12% Per annum?
A. Rs 9000.30B. Rs 9720C. Rs 10123.20D. Rs 10483.20E. None of these

Answer & Explanation
Answer: Option E

Explanation:

C.I = [25000 × (1+12/100)^3-25000]


= Rs [(25000 × 28/25 × 28/25 × 28/25)-25000]

=Rs(175616/5-25000) = Rs (35123.20 – 25000)

= Rs 10123.20

44)The Compound interest on Rs 16000 for 9 months at 20% P.a compounded quarterly is:
A. Rs 2518B. Rs 2520C. Rs 2522D. Rs 2524

Answer & Explanation
Answer: Option C

Explanation:

P = Rs 16000, R = (10/2)%


per quarter, t = 3 quarters

C.I = Rs [16000 × (1+ 5/100)^3-16000)

= Rs [16000 × 21/20 ×21/20× 21/20- 16000)

=Rs (18522-16000)=Rs 2522

45)The difference between compound interest and simple interest on a sum for 2 years at 8% P.a is Rs 786. The sum is:
A. Rs 100000B. Rs 11000C. Rs 120000D. Rs 170000

Answer & Explanation
Answer: Option C

Explanation:

Let the sum be Rs x.

Then S. I = Rs (x × 8/100 × 2) = Rs 4x/25

C. I = Rs [x × (1 + 8/100)2 - x]

= Rs (x × 27/25 × 27/25 - x)

=Rs 104x/625 (C.I) – (S.I)

= Rs(104x/625 – 4x /25)

= Rs 4x /625

 Therefore 4x/625 = 768

=> x = ((768 ×625)/4) = 120000

Therefore sum = Rs 120000

46) If the rate of interest be 4% per annum for first year 5% per annum for the second year and 6% per annum from the third year then the compound interest of Rs 10000 for 3 years will be
A. Rs 1575.20B. Rs 1600C. Rs 1625.80D. Rs 2000

Answer & Explanation
Answer: Option A

Explanation:

Amount = Rs[10000 × (1 + 4/100) × (1 +5/100) × (1 × 6/100)]


= Rs(1000 × 26/25 × 21/20 × 53/50)

= Rs (57876/5) = Rs 11575.20

C.I = Rs (11575.20 - 10000) = Rs 1575.20

47)A man deposited Rs 6000 in a bank at 5% P.a simple interest another man deposits Rs 5000 at 8% P.a Compounded interest. After 2 years the difference of their interest will be
A. Rs 230B. Rs 232C. Rs 600D. Rs 832

Answer & Explanation
Answer: Option B

Explanation:

S.I = Rs (6000 × 5/100 × 2) = Rs 600


C.I = Rs [5000 × (1 + 8/100)^2 - 5000]

= Rs (5000 × 27/25 × 27/25 - 5000)

= Rs(5832 - 5000)

= Rs 832

(C.I) – (S.I) = Rs (832 - 600) = Rs 232

48)At what rate of interest will be Rs 20000 becomes Rs 24200 after 2 years when interest is compounded annually?
A. 5%B. 6%C. 10%D. 15%

Answer & Explanation
Answer: Option C

Explanation:

P = Rs 20000, A =Rs 24200,


t = 2 years 20000 × (1 + R/100)^2 = 24200

=> (1 + R/100) 2 = 24200/20000 = 121/100 = (11/10)^2

=> 1 + R/100 = 11/10

=> R/100 = (11/10 - 1) = 1/10

=> R = (100 × 1/10) % p.a = 10 % p.a

Hence, Rate = 10 % p.a

49)A sum of money amounts to Rs. 10648 in 3years and Rs. 9680 in 2 years. The rate of interest is?
Explanation:

P be the principle and R % Per annum be the rate.


P(1 + R/100)^3 = 10648 - (i)

P(1 + R/100)^2 = 9680 - (ii)

 By dividing (i) and (ii)

(1 +R/100) = 10648/9680 Or

R/100 = 968/9680 = 1/10 or

R = 10 %

50)What will be the compound interest on Rs 25000 after 3 years at 12% Per annum?
Explanation:

C.I = [25000 × (1+12/100)^3-25000]


= Rs [(25000 × 28/25 × 28/25 × 28/25)-25000]

=Rs(175616/5-25000) = Rs (35123.20 – 25000)

= Rs 10123.20