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This mock test of Olympiad Test: Compound Interest for Class 7 helps you for every Class 7 entrance exam.
This contains 20 Multiple Choice Questions for Class 7 Olympiad Test: Compound Interest (mcq) to study with solutions a complete question bank.
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QUESTION: 1

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

Solution:

Amount = Rs [7500 × (1 + 4/100)²]

= Rs (7500 × 26/25 × 26/25)

= Rs 8112

C.I. = Rs (8112 – 7500)

= Rs 612

QUESTION: 2

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

Solution:

Principal = Rs 16, 000;

Time = 9 months = 3 quarters;

Amount = Rs [16000 × (1+5/100)³]

= [16000 × 21/20 × 21/20 × 21/20]

= Rs 18522

C.I = Rs (18522 – 16000)

= Rs 2522

QUESTION: 3

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

Solution:

C.I. = Rs [4000 × (1+10/100)² – 4000]

= Rs (4000 × 11/10 × 11/10 – 4000)

= Rs 840

Sum = Rs [420 × 100 /3 × 8] = Rs 1750

QUESTION: 4

Anil invested an amount of Rs 8000 in a fixed deposit scheme for 2 years at compound interest rate 5% per annum. How much amount will Anil get on maturity of the fixed deposit?

Solution:

Amount = Rs [8000 × (1+5/100)²]

= Rs [8000 × 21/20 × 21/20]

= Rs 8820

QUESTION: 5

The present worth of Rs 169 due in 2 years at 4% per annum compound interest is:

Solution:

Present worth = Rs [169/(1+4/100)²]

= Rs (169 × 25/26 × 25/26)

= Rs 156.25

QUESTION: 6

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:

Solution:

Difference in C.I and S.I for 2 years

= Rs (6 96.30 – 660)

= Rs 36.30

S.I for one year =Rs 330

S.I on Rs 330 for 1 year = Rs 36.30

Rate = (100 × 36.30/330 × 1)% = 11%

QUESTION: 7

The difference between simple interest and compound interest on Rs 1200 for one year at 10% per annum reckoned half yearly is

Solution:

S.I = Rs (1200 × 10 × 1/100)

= Rs 1 20

C.I = Rs [1200 × (1+5/100)² – 1200]

= Rs 123

Difference = Rs [123 – 120] = Rs 3

QUESTION: 8

A sum of money invested at compound interest amounts to Rs 800 in 3 years and to Rs 840 in 4 years. The rate of interest per annum is

Solution:

S.I. on Rs 800 for 1 year = Rs [840 – 800]

= Rs 40

Rate = (100 × 40/800 × 1)%

= 5%

QUESTION: 9

If the simple interest on a sum of money for 2 years at 5% per annum is Rs 50, what is the compound interest on the same at the same rate and for the same time?

Solution:

Sum = Rs (50 × 100/2×5)

= Rs 500

Amount = [Rs (500 × (1 + 5/100)²]

= Rs (500 × 21/20 × 21/20)

= Rs 551.25

C.I = Rs (551.25 – 500)

= Rs 51.25

QUESTION: 10

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

Solution:

Principal = Rs 1000

Amount = Rs 1331

Rate = Rs 10% p.a.

Let the time be n years. Then

Therefore n = 3 years.

QUESTION: 11

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.

Solution:

Clearly, Rate = 5% p.a.

Time = 3 years

S.I = Rs 1200.

So, Principal = Rs (100 × 1200/3× 5)

= Rs 8000

Amount = Rs [8000 × (1+ 5/100)³]

= Rs (8000 × 21/20 × 21/20 × 21/20)

= Rs 9261

C.I = Rs (9261 – 8000)

= Rs 1261

QUESTION: 12

What will be the compound interest on a sum of Rs 25,000 after 3 years at the rate of 12% per annum?

Solution:

Amount = Rs (25000 × (1+12/100)³

= Rs (25000 × 28/25 × 28/25 × 28/25)

= Rs 35123.20.

C.I = Rs (35123.20 – 25000)

= Rs 10123.20

QUESTION: 13

The compound interest on Rs 30,000 at 7% per annum is Rs 4347. The period (in years) is

Solution:

Amount = Rs (30000 + 4347)

= Rs 34347

Let the time be n years.

Then, 30000(1+7/100)^{n} = 34347

⇒ (1+7/100)^{n} = 34347/3000

⇒ (107/100)^{n} = 11449/1000

⇒(107/100)^{n} = (107/100)^{2}

Therefore = 2 years

QUESTION: 14

The difference between compound interest and simple interest on an amount of Rs 15,000 for 2 years is Rs 96. What is the rate of interest per annum?

Solution:

[15000 (1+ r/100)^{2} – 15000] – (15000 × r × 2)/100 = 96

By solving the above equation

r^{2} = (96 × 2)/3 = 64

Therefore r = 8%

QUESTION: 15

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:

Solution:

Let the sum be Rs P.

Then, [P (1 + 10/100)^{2} – P] = 525

P = (11/10)^{2} – 1 = 525

P = (525 × 100)/21 = 2500

Therefore, sum = Rs 2500

S.I. = (2500 × 5 × 4)/100 = Rs 500

QUESTION: 16

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

Solution:

Let the rate be r% p.a.

Then, 1200 × (1 + R/100)^{2} =1348.32

(1 + R/100)^{2} = 11236/10000

(1 + R/100)^{2} = (106/100)^{2}

Therefore r = 6%

QUESTION: 17

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

Solution:

P(1 + 20/100)^{n} > 2P (6/5)^{n} > 2

Now, (6/5 × 6/5 × 6/5 × 6/5) > 2

So, n = 4 years

QUESTION: 18

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

Solution:

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: 19

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?

Solution:

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. = Rs [12000 × (1 +10/100)^{3} – 1]

= 3972

QUESTION: 20

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

Solution:

Amount = [Rs1600 × (1 + 5/2 ×100)^{2} +Rs 1600 × (1 +5/2 ×100)]

= Rs 3321

∴ C.I.= Rs (3321 – 3200) = Rs 121

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