Question 1

The compound interest on rs.30000 at 7% per annum is Rs.4347. The period is

Accepted Answer

2 years

Question 2

A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.

Accepted Answer

Let the sum be Rs.P.then P(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii) On dividing,we get (1+R/100)^3=10025/6690=3/2. Substituting this value in (i),we get: P*(3/2)=6690 or P=(6690*2/3)=4460 Hence,the sum is rs.4460.

Question 3

The difference between compound interest and simple interest on a certain sum of money for 2 years at 5% per annum is Rs. 41. What is the sum of money?

Accepted Answer

Rs.16400

Question 4

Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly.

Accepted Answer

824.32

Question 5

What is the rate of interest p.c.p.a.? I. An amount doubles itself in 5 years on simple interest. II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400. III. Simple interest earned per …

Accepted Answer

I . P * R * 5 100 = P ⇔ R = 20 I I . P 1 + R 100 2 - P - P * R * 2 100 = 400 = > p R 2 = 4000000 I I I . P * R * 1 100 = 2000 = > P R = 200000 P R 2 P R = 4000000 200000 ⇔ R = 20 Thus I only or (II and III) give answer. Correct answer is (D)

Question 6

What annual payment will discharge a debt of Rs.7620 due in 3years at 1623 % per annum interest?

Accepted Answer

Let each installment be Rs.x. Then, (P.W. of Rs.x due 1 year hence) + (P.W of Rs.x due 2 years hence) + (P.W of Rs. X due 3 years hence) = 7620. x 1 + 50 3 x 100 + x 1 + 50 3 x 100 2 + x 1 + 50 3 x 100 3 = 7620 6 x 7 + 36 x 49 + 216 x 343 = 7620 294 x + 252 x + 216 x = 7620 x 343 => x = 3430 Amount of each installment = Rs.3430

Question 7

The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum

Accepted Answer

Compound Interest on P at 10% for 2 years when interest is compounded half-yearly = P 1 + R 2 100 2 T - P = P 1 + 1 20 4 - P = P 21 20 4 - P Simple Interest on P at 10% for 2 years = P R T 100 = P × 10 × 2 100 = P 5 Given that difference between compound interest and simple interest = 124.05 P * 21 20 4 - P - P 5 = 124 . 05 => P 21 20 4 - 1 - 1 5 = 124 . 05 P=8000

Question 8

If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.

Accepted Answer

Clearly, Rate = 5% p.a ., Time = 3 years S.I =Rs.1200. So,Principal =Rs.(100 x 1200/3x5) =Rs.8000. Amount =Rs.[8000 x (1+5/100)³] =Rs(8000x21/20x21/20x21/20) = Rs.9261 C.I =Rs.(9261-8000) =Rs.1261.

Question 9

A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent

Accepted Answer

Interest for 1 year is the same whether it's simple interest or the compound interest. Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225 if 100 is the principal interest =(1225/7350) * 100 = 50/3 % When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100 Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 % Therefore amount after 2 years = 100 + 325/9 = 1225/9 If 1225/9 is the amount principal =100 if 7350 is the amount principal =(900/1225)*7350 =5400 So sum = 5400; Rate = 50/3 %

Question 10

Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quartely.

Accepted Answer

Principal = Rs.16,000; Time=9 months = 3 quarters; Amount =Rs.[16000x(1+5/100)³] =[16000x21/20x21/20x21/20] = Rs.18522. C.I = Rs.(18522 - 16000) = Rs.2522.

Question 11

A sum is being lent at 20 % per annum compound interest.what is the ratio of increase in amount of 4th year to 5th year?

Accepted Answer

P 1 + r 100 4 P 1 + r 100 5 = 1 1 + r 100 = 100 100 + r = 100 120 = 5 6

Question 12

The compound interest on a sum of money for 2 years is rs.832 and the simple interest on the same sum for the same period is rs.800 .the difference between the compound interest and simple interest for 3 years

Accepted Answer

difference in C.I and S.I in 2years =Rs.32 S.I for 1year =Rs.400 S.I for Rs.400 for one year =Rs.32 rate=[100*32)/(400*1)%=8% difference between in C.I and S.I for 3rd year =S.I on Rs.832= Rs.(832*8*1)/100=Rs.66.56

Question 13

In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually?

Accepted Answer

Question 14

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate

Accepted Answer

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= R s . 12000 * 1 + 10 100 3 - 1 =Rs.3972

Question 15

On a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is

Accepted Answer

Difference in C.I and S.I for 2 years = Rs(696.30-660) =Rs. 36.30. S.I for one years = Rs330. S.I on Rs.330 for 1 year =Rs. 36.30 Rate = (100x36.30/330x1)% = 11%

Question 16

The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is Rs. 56. Then the sum is :

Accepted Answer

We know thatThe Difference between Compound Interest and Simple Interest for n years at R rate of interest is given by C . I n - S . I n = P R 100 n Here n = 2 years, R = 20%, C.I - S.I = 56 56 = P 20 100 2 = > P = 56 x 5 2 = > P = 56 x 25 = > P = Rs . 1400

Question 17

The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?

Accepted Answer

The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 during three year span. Therefore, the rate of growth for three years has been constant. The rate of growth during the next three years will also be the same. Therefore, the population will grow from 4800 by 4800 * 1 3 = 1600 Hence, the population three years from now will be 4800 + 1600 = 6400

Question 18

Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually

Accepted Answer

Amount = Rs[7500x(1+4/100)²] =Rs.(7500 * 26/25 * 26/25) =Rs.8112 C.I = Rs(8112 - 7500) =Rs.612

Question 19

Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.

Accepted Answer

Let the two parts be Rs. x and Rs. (1301 - x). x 1 + 4 100 7 = 1301 - x 1 + 4 100 9 x 1301 - x = 1 + 4 100 2 = 26 25 * 25 26 => 625x=676(1301-x) 1301x=676 x 1301x=676. So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625

Question 20

A certain sum is to be divided between A and B so that after 5 years the amount received by A is equal to the amount received by B after 7 years. The rate of interest is 10%, interest compounded annually. Find the ratio of amounts invested by them.

Accepted Answer

121:100

Compound Interest Questions