Question 1

The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned ?

Accepted Answer

Let the sum be Rs. P P{ 1 + 8 100 2 - 1 } = 2828.80 It is in the form of a 2 - b 2 = a + b a - b P(8/100)(2 + 8/100) = 2828.80 P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80

Question 2

A sum of Rs. 8,000 is deposited for 3 years at 5% per annum compound interest (compounded annually). The difference of interest for 3 years and 2 years will be

Accepted Answer

Given principal amount = Rs. 8000 Time = 3yrs Rate = 5% C.I for 3 yrs = 8000 x 105 100 x 105 100 x 105 100 - 8000 = Rs . 1261 Now, C.I for 2 yrs = 8000 x 105 100 x 105 100 = Rs . 820 Hence, the required difference in C.I is 1261 - 820 = Rs. 441

Question 3

The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

Accepted Answer

P 1 + 20 100 n > 2 P ⇔ 6 5 n > 2 6 5 × 6 5 × 6 5 × 6 5 > 2 so, answer is 4 years

Question 4

If the compound interest on a certain sum at 1623 % to 3 years is Rs.1270, find the simple interest on the same sum at the same rate and f or the same period.

Accepted Answer

Let the sum be Rs. x. Then, C . I = x * 50 300 * 100 3 - x = 343 x 216 - x = 127 x 216 ⇔ 127 x 216 = 1270 x = 2160 Thus, the sum is Rs. 2160 S . I = R s . 2160 * 50 3 * 3 * 1 100 = R s 1080

Question 5

Simple interest on a certain sum at 7% per annum for 4 years is Rs. 2415. What will be the compound interest on the same principal at 4% per annum in two years?

Accepted Answer

We know that, S . I . = PTR 100 ⇒ P = S . I x 100 T x R And also , C . I = P 1 + R 100 n - 1 From given data, P = Rs. 8625 Now, C.I = 8625 1 + 4 100 2 - 1 = 8625 26 25 2 - 1 = 8625 676 625 - 1 = 8625 x 51 625 C . I = Rs . 703 . 80

Question 6

Sonika invested an amount of Rs.5800 for 2 years. At what rate of compound interest will she get an amount of Rs.594.50 at the end of 2 years ?

Accepted Answer

C.I = P 1 + r 100 t - 1 594.5 = 5800 1 + r 100 2 - 1 594 . 5 5800 + 1 = 1 + r 100 2 r 100 = 1 . 05 - 1 = 0 . 05 = > r = 5 % .

Question 7

The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is ?

Accepted Answer

P 1 + 20 100 n > 2P Now, (6/5 x 6/5 x 6/5 x 6/5) > 2. So, n = 4 years.

Question 8

The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?

Accepted Answer

when interest is reckoned using compound interest, interest being compounded annually. The difference in the simple interest and compound interest for two years is on account of the interest paid on the first year's interest Hence 12% of simple interest = 90 => simple interest =90/0.12 =750. As the simple interest for a year = 750 @ 12% p.a., the principal =750/0.12 = Rs.6250. If the principal is 6250, then the amount outstanding at the end of 3 years = 6250 + 3(simple interest on 6250) + 3 (interest on simple interest) + 1 (interest on interest on interest) = 6250 +3(750) + 3(90) + 1(10.80) = 8780.80.

Question 9

Rs.100 doubled in 5 years when compounded annually. How many more years will it take to get another Rs.200 compound interest

Accepted Answer

Rs.100 invested in compound interest becomes Rs.200 in 5 years. The amount will double again in another 5 years. i.e., the amount will become Rs.400 in another 5 years. So, to earn another Rs.200 interest, it will take another 5 years.

Question 10

Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit

Accepted Answer

Amount = R s . 8000 * 1 + 5 100 2 =Rs.8820

Question 11

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

Accepted Answer

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

Question 12

Find the C.I. on Rs. 15,225 for 9 months at 16% per annum compounded quarterly ?

Accepted Answer

P = Rs. 15225, n = 9 months = 3 quarters, R = 16% p.a. per quarter. Amount = 15225 x 1 + 4 100 3 = (15225 x 26/25 x 26/25 x 26/25) = Rs. 17126.05 => C.I. = 17126 - 15625 = Rs. 1901.05.

Question 13

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is

Accepted Answer

Let the sum be Rs. P. Then,[p(1+10/100)2-p]=525 Sum =Rs.2500 S.I.= Rs.(2500*5*4)/100 = Rs. 500

Question 14

If you deposit $4000 into an account paying 6% annual interest compounded quarterly, how much money will be in the account after 5 years ?

Accepted Answer

The mathematical formula for calculating compound interest depends on several factors. These factors include the amount of money deposited called the principal, the annual interest rate (in decimal form), the number of times the money is compounded per year, and the number of years the money is left in the bank. F V = p 1 + r n n t FV = Future value of the Deposit p = Principal or Amount of Money deposited r = Annual Interest Rate (in decimal form ) n = No of times compounded per year t = time in years F V = 4000 1 + 0 . 06 4 4 ( 5 ) = 5387.42

Question 15

Calculate the amount on Rs. 1875 for 2 year at 4% per annum, compounded yearly.

Accepted Answer

Amount = P(1 + r/100)^t Amount = 1875(1 + 4/100)^2 Amount = 1875(104/100)(104/100) Amount = 2028

Question 16

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the …

Accepted Answer

Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year. The extra interest earned on the compound interest bond = Rs.55 The interest for the first year =550/2 = Rs.275 Therefore, the rate of interest = 55 275 * 100 = 20% p.a. 20% interest means that Shawn received 20% of the amount he invested in the bonds as interest. If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the bonds = 275 20 * 100 = 1375. As he invested equal sums in both the bonds, his total savings before investing = 2 x 1375 =Rs.2750.

Compound Interest Questions