Question 1

Vandana invested an amount of ₹ 8000 in a fixed deposit scheme for 2 yr at the rate of 5% pa compound interest. How much amount will Vandana get on maturity of the fixed deposit?

Accepted Answer

Given, P = ₹ 8000, R = 5% and n = 2 Yr According to the formula, Amount = p ( 1 + R / 100 )n = 8000 ( 1 + 5/100 )2 = 8000 x (105/100)2 =8000 x (21/20) x (21/20) = 20 x 21 x 21 = ₹ 8820

Question 2

Raja invested ₹ 15000 at the rate of 10 % pa for 1 yr. If the interest is compound half-yearly, then find the amount received by Raja at the end of the year.

Accepted Answer

Given P = ₹ 15000 , R = 10 % and n = 1 yr Accounting to the formula, Amount = P(1 + R/(2 x 100))2n = 15000 x (1 + 5/100 )2 = 15000 x (105/100 )2 = 15000 x (21/20) x (21/20) = ₹ 16537.50

Question 3

What amount will be received on a sum of Rs 15000 in 1 1/ 4 yr at 12% pa, if interest is compounded quarterly?

Accepted Answer

Given, P = Rs 15000, R = 12 % and n = 11/4 = 5/4 Yr According to the formula, Amount = p [1 + R/(100 x 4)]4n = 15000 x [1 + 12/(100 x 4)]4 x 5/4 = 15000(412/400)5 = 15000 (103/100)5 = 15000 x (103/100) x (103/100) x (103/100) x (103/100) x (103/100) = (15 x 103 x 103 x 103 x 103 x 103) / 10000000 = Rs 17389.111 = Rs 17389.12 (approx )

Question 4

The compound interest on ₹ 30000 at 7% pa for a certain time is ₹4347. The time is

Accepted Answer

Given, CI = ₹ 4347, P = ₹ 30000 and R = 7% By formula, CI = P[(1 + R/100)n - 1 ] ⇒ 4347 = 30000 [(1+7/100)n - 1] ⇒ (107/100)n = (4347/30000) + 1 ⇒ (107/100)n = 34347/30000 = 11449/10000 ⇒ (107/100)n = (107/100)2 ∴ n = 2

Question 5

What is the difference between compound interest and simple interest for 2 yr on the sum of ₹ 1250 at 4% pa?

Accepted Answer

Given, P = ₹ 1250, n = 2 yr and R = 4% According to the formula, Difference between compound interest and simple interest = PR2/1002 ∴ Required difference = (1250 x 4 x 4)/(100 x 100) = ₹ 2

Question 6

The difference between compound and simple rates of interest on ₹ 10000 for 3 yr at 5% per annum is

Accepted Answer

Required difference = P(R/100)2 x [(300 + R)/100] = 10000(5/100)2 (305/100) = 76.25

Question 7

A borrowed sum was paid in the two annual installments of ₹ 121 each. If the rate of compound interest is 10% pa, what sum was borrowed?

Accepted Answer

According to the question, Borrowed sum = [121/{1/(1 + 10/100)}] + 121/(1 + 10/100)2 = 121/(11/10) + 121/{(11/10) x (11/10)] =110 + 100 = ₹ 210

Question 8

If ₹ 3000 amounts to ₹4329 at compound interest in a certain time , then ₹ 3000 amounts to what inhalf of the time?

Accepted Answer

Let rate = R% and time = n yr Then, 4320 = 3000(1+R/100)n ⇒ (1+R/100)n = 4320/3000 = 1.44 ∴ (1 + R/100)n/2 = √1.44 = 1.2 ∴ Required amount for n/2 yr = 3000(1+ R/100)n/2 = 3000 x 1.2 = ₹ 3600

Question 9

The population of a city increases at the rate of 5% pa. If the present population of the city is 185220, then what was its population 3 yr ago?

Accepted Answer

Given, P = 185220 R = 5% (increases) and n = 3 yr According to the formula, Population n yr ago = P/(1 + R/100)n = 185220/(1 + 5/100)3 = 185220/[(21/20) x (21/20) x (21/20)] = [185220 x 20 x 20 x 20] / [21 x 21 x 21] = 20 x 20 x 20 x 20 = 160000

Question 10

A sum of ₹ 400 amounts to ₹ 441 in 2 yr. What will be its amount, if the rate of interest is increased by 5%?

Accepted Answer

According to the given condition. 441 = 400 (1 + R/100)2 ⇒ 441/400 = (1 + R/100)2 ⇒ (21/20)2 = (1 + R/100)2 ⇒ 21/20 = 1 + R/100 ⇒ (21/20) - 1 = R/100 ⇒ R/100 = 1/20 ∴ R = 5% ∴ new rate = 5 + 5 = 10% ∴ Amount = 400 (1 + 10/100)2 = 400 x (11/10) x (11/10) = ₹ 484

Question 11

The cost price of an LCD TV set is ₹ 100000. If its price value depreciates at the rate of 10% pa. then what will be the price at the end of 3 yr?

Accepted Answer

Given P = ₹ 100000, R = 10%, n = 3 yr According to the formula, Price of LCD TV set after 3 yr. = P(1 - R/100)n = 100000 (1 - 10/100)3 = 100000(90/100)3 = 100000 x (9/10) x (9/10) x (9/10) = ₹ 72900

Question 12

A sum, at the compound rate of interest, becomes 2 1/ 2 times in 6 yr. The same sum becomes what times in 18 yr?

Accepted Answer

If sum is P, then P becomes 5P/2 in 6 yr. 5P/2 becomes 25P/4 in 12 yr. 25P/4 becomes 125P/8 in 18 yr. The sum becomes 125/8 times in 18 yr.

Question 13

If the difference between the compound interest and simple interest on a sum of money at 5% pa for 2 yr is ₹ 16, then find the simple interest?

Accepted Answer

Given, CI - SI = 16, R = 5%, n = 2 yr and SI = ? According to the formula, CI - SI = (SI x R)/200 ⇒ 16 = (SI x 5)/200 ⇒ 16 = SI/40 ∴ SI = ₹ 640

Question 14

The compound interest is ₹ 6.40 more than the simple interest, if a sum is lent for 2 yr at 8% compound interest. Find the sum.

Accepted Answer

Here, D = ₹6.40, R = 8% and n = 2 yr Then, according to the formula, Difference between compound interest and simple interest D = PR2 / 1002 ⇒ 6.40 = P x 64/10000 ∴ P = ₹ 1000

Question 15

A certain sum at compound interest amounts to ₹ 12960 in 2 yr and ₹ 13176 in 3 yr. Find the rate per cent per annum.

Accepted Answer

SI for on ₹ 12960 for 1 yr = 13176 - 12960 = ₹ 216 By formula, SI = (P x R x T)/ 100 ⇒ 216 = (12960 x R x 1)/100 ∴ R = 5/3 = 12/3

Question 16

The simple interest on a certain sum for 2 yr is ₹ 120 and compound interest is ₹ 129. Find the rate of interest.

Accepted Answer

Here, n = 2 yr, SI = ₹ 120 and CI = ₹ 129 CI = SI (1+ R/200) ⇒ 129 = 120(1 + R/200) ⇒ 129/120 = 1 + R/200 ⇒ (129/120) - 1 = R / 200 ⇒ 9/120 = R/200 ∴ R = (9 x 200)/120 = 15%

Question 17

The height of a tree increases every year 1/8 times. If the present height of the tree is 64 cm, then what will be its height after 2 yr?

Accepted Answer

Percentage growth = (1/8) x 100 % = 12.5% Height after 2 yr = 64 x (1+ 12.5/100)2 = 64 x (9/8) x (9/8) = 81 cm

Question 18

An amount at the rate of 5% pa becomes ₹ 10 more at compound interest than that of simple interest after 2 yr. Calculate the principal.

Accepted Answer

Here, CI - SI = 10, R = 5%, n = 2 yr and P = ? According to the formula, CI - SI = PR2/1002 ⇒ 10 = (P x 25)/10000 ∴ P = (400 x 10) = ₹ 4000

Question 19

The principal amount which yields a compound interest of ₹ 208 in the second year at 4% is

Accepted Answer

Let the principal be ₹ P. Amount after first year = (P x 104)/100 and amount after second year P x (104/100) x (4/100) According to the question. (P x 104 x 4)/(100 x 100) = 208 ∴ P = ₹ 5000

Question 20

Find the compound interest for a sum of ₹ 9375 in 2 yr, if the rate of interest for the first year is 2% and for the second year is 4%.

Accepted Answer

Given, P = ₹ 9375, R1 = 2% and R2 = 4% According to the formula, A = P (1 + R1/100) (1 + R2/100) = 9375 (1 + 2/100) (1 + 4/100) = 9375 x (51/50) x (26/25) = 7.5 x 51 x 26 = ₹ 9945 Now CI = A - P = 9945 - 9375 = ₹ 570

Compound Interest Questions