Question 1

If Rs. 7500 are borrowed at compound interest at the rate of 4% per annum, then after 2 years the amount to be paid is?

Accepted Answer

Amount = Rs. 7500(1 + 4/100)2 = Rs. 7500 x 26/25 x 26/25 = Rs .8112

Question 2

A sum amounts to Rs. 3149.29 in 3 years at compound interest. The sum is?

Accepted Answer

Let P be the principle and R% per annum be rate Then, P(1 +R/100)3 = 3149.28 .....(i) and P(1 + R/100)2 = 2916 .....(ii) on dividing(i) and (ii) we get ∴ (1 + R/100) = 3149.28/2916 ⇒ R/100 = 233.28/2916 ⇒ R = 233.28/2916 x 100 = 8% Now, P(1 + 8/100)2 = 2916 ⇒ P x 27/25 x 27/25 = 2916 ∴ P = (2916 x 25 x 25)/(27 x 27) = Rs. 2500

Question 3

A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times itself in?

Accepted Answer

Let the principal be P and rate be r%.Then 2P = P(1 + r/100)5 ⇒ (1 + r/100)5 = 2 Let it be 8 times in t years, then ∵ 8P = P(1 + r/100)t ⇒ (1 + r/100)t = 8 ⇒ (2)3 ⇒ (1 + r/100)15 ∴ t =15 year.

Question 4

The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 420. The simple interest on the same sum at the same rate and for the same time will be?

Accepted Answer

Let the principal be P. Then, ∵ P(1 +10/100)2 - P =420 ⇒ P(121 - 100/100) =420 ⇒ P = Rs. 2000 ∴ Requared S.I.= Rs.(2000 x 2 x 10)/100 = Rs. 400

Question 5

Rs. 1600 at 10% per annum compounded half yearly amount to Rs. 1944.81 in?

Accepted Answer

1600(1 +5/100)t = 1944.81 ⇒ (21/20)t =194481/160000 =(441/400)2 = (21/20)4 ∴ T = 4( half years) ⇒ Required time =2 years

Question 6

What will be the approximate compound interest on Rs. 101005 at 10% p.a. for 3 years?

Accepted Answer

Compound interest = P {(1 + r/100)t - 1} = 10105 { (1 +10/100)3 - 1} =10105 {(11/10)3 - 1} =10105 {1331/1000 - 1} =10105(331/1000) = 3344.755 = Rs. 3300(app.)

Question 7

If the compound interest of a certain sum of money for two successive years be Rs, 225 and Rs. 238.50. What is the rate of interest per annum?

Accepted Answer

From question it is clear that the simple interest of rupees 225 for one year is 238.50 - 225. So Rate = (simple interest x 100 )/( time x principle) = {(238.50 - 225) x 100}/(225 x 1) % = 6%

Question 8

A moneylender lends Rs. 2000 for 6 months at 20% per annum whereas the interest is compounded quarterly. After the given period he will get the amount of?

Accepted Answer

For the quarterly interest, Time = (6/12) year x 4 = 2 quarterly Rate = 20/4 = 5% (∴ On quarterly interest time is multiplied by 4 and rate is divided by 4) Hence,required amount = Principal (1 + Rate/100)Time = 2000(1 +5/10)2 = 2000(21/20)2 = Rs. 2205

Question 9

In what time will Rs. 6250 amount to Rs. 6632.55 at 4% compound interest payable half yearly?

Accepted Answer

Since Interest accumulates half yearly so effective rate = R/2 = 4/2 = 2. And effective time is 2t. ∵ 6250 [1 + 2/100]2t = 6632.55 ⇒ (1 +2/100)2t = 663255/625000 = 132651/125000 = (51/50)3 ⇒ (51/50)2t = (51/50)3 ⇒ 2t =3 ∴ t = 3/2 years

Question 10

Find the effective annual rate of 4 per cent per annum compound interest paid quarterly.?

Accepted Answer

Effective annual rate = 100(1 + {(4/4) /100})4 - 100 = (101/100)4 x 100 - 100 = 104.0604 - 100 = 4.0604%

Question 11

In what time will Rs. 390625 amount to Rs. 456976 at 4 per cent compound interest?

Accepted Answer

∵ P(1 + r/100)t = A ⇒ 390625(1 + 4/100)t = 456976 ⇒ (1 + 4/100)t = 456976/390625 =(26/25)4 ⇒ (26/25)t = (26/25)4 ⇒ t = 4 ∴ The required time is 4 years.

Question 12

Find the effective annual rate of 5 per cent per annum compound interest paid half yearly?

Accepted Answer

The amount of Rs. 100 in one year at compound interest at 5% per annum payable half yearly. = Rs. 100(1 + 5/2 /100)2 =Rs. 100(102.5/100)2 =Rs. 100(1.025)2 =Rs. 105.0625 Thus, the nominal rate of 5% payable half yearly has the same effect as the rate of 5.0625 per cent would have, if payable yearly. Hence 5.0625 per cent is called the effective annual rate 5% per annum payable half yearly.

Question 13

At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

Accepted Answer

Let the rate be R% per annum. Then, 1200 x (1 + R/100)2 = 1348.32 ⇒ (1 + R/100)2 =1348.32/1200 = 1.1236 = (1.06)2 ⇒ (1 + R/100) =1.06 ⇒ R/100 = 0.06 ∴ R = 6%

Question 14

A sum of ₹ 2400 deposited at CI, Double after 5 yr. After 20 yr it will become?

Accepted Answer

2P = P (1 + R/100) 5 ⇒ 24 P = P(1 + R/100)20 ⇒ The amount becomes 24 times = 16 times and required amount = 2400 x 16 = ₹ 38400

Question 15

Rohit earns an interest of ₹ 1656 for the third year and ₹ 1440 for the second year on the same sum. Find the rate of interest if it is lent at compound interest?

Accepted Answer

Interest on ₹ 1440 = ₹ 216 for the third year ⇒ Rate percentage = (216 x 100)/(1440 x 1) = 15 %

Question 16

What will be the compound interest on a sum of ₹ 50000 after 3 yr at the rate of 12% pa?

Accepted Answer

Given, P = ₹ 50000, R = 12% and n = 3 Yr According to the formula, Amount = P (1 + R/100 )n = 50000 (1 + 12/100 )3 = 50000 x (28/25) x (28/25) x (28/25) = 16 x (28 x 28 x 28)/ 5 = 351232/5 = ₹ 70246.40 ∴ CI = 702446.40 - 50000 = ₹ 20246.40

Question 17

A sum amounts to ₹ 1352 in 2 yr at 4% compound interest. The sum is

Accepted Answer

Using the formula, A = p ( 1 + R/100 )n ⇒ 1352 = p(1 + 4/100 )2 ⇒ 1352 = p(1.04 )2 ∴ p = 1352/(1.04)2 = ₹ 1250

Question 18

What will be the present worth of ₹ 169 due in 2 yr at 4 % pa compound interest?

Accepted Answer

Given R = 4 %, n = 2 yr and A = ₹ 169. P = ? Amount = P(1 + R/100)n ⇒ 169 = P(1 + 4/100 )2 ⇒ 169 = P(26/25)2 ⇒ P = 169 x (25 x 25)/(26 x 26) ∴ P = 105625 / 676 = ₹ 156.25

Question 19

Find the compound interest on ₹ 31250 at 16 % pa compounded quaterly for 9 months.

Accepted Answer

Given, P = ₹ 31250, n = 9 Month = 3 quarters and R = 16% pa = 4% per quarter According to the formula Amount = P(1 + R/100 )n = 31250(1 + 4/100 )3 = 31250 x (26/25) x (26/25) x (26/25) = ₹ 35150 ∴ CI = 35152 - 31250 = ₹ 3902

Question 20

A sum amounts to ₹ 2916 in 2 yr and ₹ 3149.28 in 3 yr at compound interest. The sum is?

Accepted Answer

Let required amount be ₹ P. According to the question, 2916 = P (1 + R/100)2 ... (i) and 3149.28 = P(1 + R/100)3 ... (ii) On dividing Eq. (ii) by Eq. (i), we get 1 + R/100 = 3149.28/2916 ⇒ R/100 = (3149.28/2916) - 1 ⇒ R = (233.28/2916) x 100 = 8% From Eq. (i), P = (2916 x 100 x 100)/(108 x 108) = ₹ 2500

Compound Interest Questions