Question 1

The population of a country is 100 crore and it is the possibility that the population will become 13.31 crore in 3 yr. What will be the annual rate percent on this growth?

Accepted Answer

Given, P = 10 crore and population after 3 yr = 13.31 crore According to the formula, Population after n yr = P (1 + R/100 )n ⇒ 13.31 = 10 (1 + R/100 )3 ⇒ 1331/1000 = (1 + R/100 )3 ⇒ (11/10)3 = (1 + R/100 )3 ⇒ 1 + R/100 = 11/10 ⇒ R/100 = 11/10 - 1 = 1/10 ∴ R = 10%

Question 2

If the different between the compound interest and the simple interest on a certain sum for 2 yr at 8% per annum is ₹ 32, then the sum is

Accepted Answer

Given, R = 8%, D = ₹ 32 and P = ? By formula, D = P(R/100)2 ⇒ 32 = P(8/100)2 ∴ P = 32 x [(100 x 100)/(8 x 8)] = ₹ 5000

Question 3

What will be the principle, if the rate of 5% per annum can yield ₹ 410 as compound interest in 2 yr?

Accepted Answer

Let the amount be ₹ P R = 5%, n = 2 yr and CI ₹ 410 By formula, CI = P [ (1 + R/100)n - 1 ] ⇒ 410 = P [ (1 + 5/100)2 - 1] ⇒ 410 = P [ (1 + 1/20)2 - 1] ⇒ 410 = P [ (21/20)2 - 1] ⇒ 410 = P [ 441/400 - 1 ] ⇒ 410 = P [(441 - 400) /400] = P x 41/400 ⇒ P = (410 x 400)/41 ∴ P = ₹ 4000

Question 4

At what per cent annual compound interest, rate, a certain sum amounts to its 27 times in 3 yr?

Accepted Answer

Let sum = P and given that n = 3 yr According to the question, Amount = 27 P According to the formula, Amount = P (1 + R/100)n ⇒ 27 P = P (1 + R/100)3 ⇒ 27 = (1 + R/100)3 ⇒ (1 + R/100)3 = (3)3 ⇒ 1 + R/100 = 3 ⇒ R/100 = 3 - 1 = 2 ∴ R = 200%

Question 5

The compound interest on Rs. 30000 at 7% per annum for a certain time is Rs. 4347. The time is?

Accepted Answer

∵ 30000 x (1 +7/100)t = 30000 + 4347 ⇒ (107/100)t = 34347/30000 ⇒11449/10000 = (107/100)2 ∴ Time = 2 years

Question 6

The difference of compound interest on Rs.800 for 1 year at 20% per annum when compound half yearly and quarterly is?

Accepted Answer

C.I. when reckoned half yearly = Rs.[800 x (1 + 10/100)2 - 800] = Rs. 168 C.I.when reckoned quarterly = Rs.800[(1 + 5/100)4 - 1] = 800[(194481 - 160000)/160000] = 34481/200 = Rs.172.40 ∵ Required difference =Rs.(172.40 - 168) = Rs.4.40

Question 7

The compound interest of Rs. 20480 at 6 1/ 4% per annum for 2 years 73 days is?

Accepted Answer

C.I. = Rs[20480 x(1 +25/4 x 100)2 (1 + 1/5 x 25/4 x 100) - 20480 ] = Rs.[(20480 x 17/16 x 17/16 x 81/80) - 20480] = 20480[23409 - 20480/20480] = Rs .2929

Question 8

The difference in compound interest and simple interest for 2 years on a sum of money is Rs. 160. If the simple interest for 2 years be Rs. 2880, the rate per cent is?

Accepted Answer

∵ S.I. for 1 year =Rs. 1440 ⇒ S.I. on Rs.1440 for 1 year = Rs.160 Hence, ∴ Rate per cent = (100 x 160) / (1440 x 1) % = 100/9% = 111/9%

Question 9

The compound interest on a sum 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 and simple interest for 3 years will be?

Accepted Answer

S.I. for first year = Rs. 400 S.I. on Rs .400 for 1 year =Rs. 32 ∴ Rate = (interest x 100)/(principle x time) = (100 x 32)/(400 x 1) = 8% Hence, the difference for 3rd year is S.I.on Rs. 832 = Rs.(832 x 8/100) = Rs. 66.56 ∴ Total difference = Rs.(32 + 66.56) = Rs. 98.56

Question 10

A man borrows Rs. 4000 from a bank at 7 1/ 2% compound interest. At the end of every he pays Rs. 1500 as part repayment of loan and interest. How much does he still owe to the bank after there such installments?

Accepted Answer

Balance = Rs.[{4000 x (1 x 15/2 x 100)3} - {1500 x (1 + 15/2 x 100)2 + 1500 x (1 + 15/2 x 100) + 1500}] = Rs. 123.25

Question 11

A sum of Rs. 550 was taken as a loan. This is to be repaid in two equal annual instalments. if the rate of interested be 20% compound annually then the value of each instalment is?

Accepted Answer

Let the value of each instalment be Rs. x Then, {x/(1 + 20/100) + x/(1 + 20/100)2} = 550 ⇒ 5x / 6 + 25x / 36 =550 ⇒ 55x / 36 = 550 ∴ x = 360

Question 12

If the simple interest on certain sum of money be Rs. 40 for 2 years and the compound interest on the same sum at the same rate and for the same time be Rs. 45. What is the principle?

Accepted Answer

S.I. for 2 year = Rs. 40 S.I. for 1 year = Rs. 20 Rate = {(C.I. for 2 year - S.I. for 2 year) / (S.I. for 1 year)} x 100 = {(45 - 40) / 20} x 100 = 25% ∴ Principal = (S.I. x 100)/(Rate x Time) = (40 x 100)/(25 x 2) = Rs. 80

Question 13

Neeraj saves Rs. 400 at the end of each year and lends this saving at 5% p.a. compound interest, How much will it worth at the end of 3 years?

Accepted Answer

Amount after 3 years = 400(1 + 5/100)3 + 400(1 + 5/100)2 + 400(1 + 5/100) = 400(1+ 5/100) {1+ 5/100)2 + (1 + 5/100) + 1 } = 400(105/100) {(105/100)2 + (105/100) + 1} = 400(21/20) {(21/20)2 + 21/20 + 1} = 400(441/400 + 21/20 + 1) = 400(441 + 420 + 400/400) = 420(1261/400) = Rs.1324.05

Question 14

If a sum of money placed at compound interest becomes 3 times of itself in 3 years. In how many years will it be 9 times at the same rate of interest?

Accepted Answer

Let the principle be P then amount be 3P ∵ 3P =P(1 + r/100)3 ⇒ 3 = (1 + r/100)3 On squaring on both the sides, ⇒ (3)2 = {(1 + r/100)3}2 ∴ 9 = (1 + r/100)6 Hence,it will become 9 times in 6 years.

Question 15

A person invested a certain amount at simple interest at the rate of 6 percent annum earning Rs. 900 as an interest at the end of three years. Had the interest been compounded every year. How much more interest would he have earned on the same amoun…

Accepted Answer

Certain sum for the person = (900 x 100)/(6 x 3) =Rs. 5000 ∴ Interest on Rs. 5000 by C.I. = 5000(1 +6/100)3 - 5000 = Rs. 955.08 ∴ More interest =Rs. (955.08 - 900) = Rs. 55.08

Question 16

The difference between the simple and the compound interest compounded every six months at the rate of 10 percent per annum at the end of two years is Rs. 124.05. What is the sum?

Accepted Answer

Let the sum be Rs. P, then ∵ [ P(1 +5/100)4 - P] - [(P x 10 x 2)/100 ] = 124.05 Solving the above equation,we get P = Rs. 8000.

Question 17

The cash price of a refrigerator is Rs. 7044. A customer paid Rs. 2000 in case and promised to pay the remaining money in 3 yearly equal instalments at the rate of 5% per annum compound interest. What is the value of each instalment?

Accepted Answer

Remaining money = 7044 - 2000 = Rs. 5044 If each installment is of Rs. P When the amount is Rs. P at the end of first, second and third year at the rate of 5% then principal will be - P/(1 + 5/100), P/(1 +5/100)2 and P/(1 +5/100)3 ∴ P/(1 +5/100) + P/(1 + 5/100)2 + P/(1 +5/100)3 = 5044 ⇒ P(20/21) + P(20/21)2 + P(20/21)3 = 5044 ⇒ P(20/21) { 1 +(20/21) + (20/21)2} = 5044 ⇒ P(20/21) {1 +20/21 +400/441} = 5044 ⇒ P(20/21) {441 + 420 + 400/441} =5044 ⇒ P(20/21) (1261/441) =5044 ∴ P = (5044 x 21 x 441)/ (20 x 1261) = Rs. 1852.20

Question 18

Vijay obtains a loan of 64000 against his fixed deposits. If the rate of interest be 2.5 paise per rupee per annum. Calculate the compound interest payable after 3 years?

Accepted Answer

P = Rs. 64000 r = 2.5 paise per rupee per annum (given) = 0.025 rupee per rupee per annum = 0.025 x 100 rupee per hundred rupee per annum = 0.025 x 100 per cent per annum = 2.5 per cent per annum t = 3 years C.I. = 6400[(1 + 2.5/100)3 - 1] = 64000[(1.025)3 - 1] = 64000[1.0769 - 1] = 64000 x 0.0769 = 4921.6 = Rs. 4921 ∴ The compound interest payable is Rs. 4921.

Question 19

Divided Rs. 3903 between A and B, so that A's share at the end of 7 years may equal to B's share at the end of 9 years, compound interest being at 4 per cent?

Accepted Answer

We have (A's present share) (1 + 4/100)7 = (B's present share) (1 + 4/100)9 ∴ A's present share/B's present share = (1 + 4/100)2 = (26/25)2 = 676/625 Dividing Rs. 3903 in the ratio of 676 : 625 ∴ A's present share = 676/(676 + 625) of Rs .3903 = Rs. 2028 B's present share = Rs. 3903 - Rs. 2028 = Rs. 1875

Question 20

Akash borrows ₹ 65000 at 10% per annum simple interest for 3 yr and lends it at 10% per annum compound interest for 3 yr , Find his gain after three years.?

Accepted Answer

SI on ₹ 65000 at the rate of 10% for 3 yr = (65000 x 10 x 3)/100 = ₹ 19500 CI on ₹ 65000 at the rate of 10% for 3 yr = 65000(1 + 10/100)2 - 65000 = 65000(11 x 11 x 11 - 10 x 10 x 10)/1000 = ₹ 21515 ∴ Required gain = 21515 - 19500 = ₹ 2015

Compound Interest Questions