Simple and Compound Interest Set 1

20 questions

Practice free Simple and Compound Interest MCQ questions with answers — easy level, covering SI formulas, doubling time, depreciation, instalment calculations, population growth and decay, and ratio-based interest problems. Simple and compound interest is a core topic in the quantitative aptitude sections of most competitive exams worldwide. Attempt all questions and check your answers instantly with clear explanations.

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A scooter worth Rs. 50,000 depreciates at 10% per annum. Find its value after two years.

View solution & Explanation

Correct Answer Rs. 40,500

Value after 1 year = 50000 - 10% of 50000 = 50000 - 5000 = 45000

Value after 2 years = 45000 - 10% of 45000 = 45000 - 4500 = 40500

So, the value of the scooter after 2 years = Rs. 40,500

If a sum of Rs. 2300 is to be repaid in two equal annual installments at 10% per annum, what is the amount of each installment?

View solution & Explanation

Correct Answer Rs. 1320

Let each installment = x

Present value of 1st installment = x/1.1 Present value of 2nd installment = x/1.2

So, x/1.1 + x/1.2 = 2300

= 10x/11 + 5x/6 = 2300

LCM of 11 and 6 = 66

= 60x/66 + 55x/66 = 2300

= 115x/66 = 2300

115x = 2300 * 66 115x = 151800

x = 151800/115 x = 1320

So, each installment = Rs. 1320

What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 8 years and that for 12 years?

View solution & Explanation

Correct Answer 2 : 3

In simple interest, when principal and rate are same, interest is directly proportional to time.

So ratio = 8 : 12

Divide both by 4:

= 2 : 3

So, the ratio is 2 : 3

How much time will it take for an amount of Rs. 800 to yield Rs. 144 as interest at 6% per annum simple interest?

View solution & Explanation

Correct Answer 3 years

Simple interest formula:

SI = P R T / 100

144 = 800 6 T / 100

144 = 48T

T = 144/48 T = 3

So, time = 3 years

A sum of money at simple interest amounts to Rs. 1260 in 4 years and to Rs. 1400 in 5 years. The sum is:

View solution & Explanation

Correct Answer Rs. 700

Difference between 5-year amount and 4-year amount = 1400 - 1260 = 140

So, 1 year interest = Rs. 140

4 years interest = 140 * 4 = 560

Principal = 1260 - 560 = 700

So, the sum is Rs. 700

The difference between the simple interest received from two different sources on Rs. 2000 for 4 years is Rs. 32. The difference between their rates of interest is:

View solution & Explanation

Correct Answer 0.4%

Difference in SI = P R T / 100

32 = 2000 R 4 / 100

32 = 80R

R = 32/80 R = 0.4

So, the difference between rates = 0.4%

In how many years will a sum of money double itself at 12.5% per annum simple interest?

View solution & Explanation

Correct Answer 8 years

To double, interest = principal

So, SI = 100% of principal

Time = 100/12.5 = 8

So, the money will double in 8 years

If a sum doubles in 20 years, how much will it be in 10 years?

View solution & Explanation

Correct Answer 1.5 times

If a sum doubles in 20 years, then interest in 20 years = principal

So, in 10 years, interest = half of principal

= P/2

Amount after 10 years = P + P/2 = 3P/2 = 1.5P

So, the amount will be 1.5 times

The population of a town decreases at the rate of 10% per annum. If its population 2 years ago was 20,000, the present population is:

View solution & Explanation

Correct Answer 16,200

Present population after 1 year = 20000 - 10% of 20000 = 20000 - 2000 = 18000

After 2 years = 18000 - 10% of 18000 = 18000 - 1800 = 16200

So, present population = 16,200

Q10

The amount Rs. 3000 becomes Rs. 3360 in 2 years at simple interest. If the interest rate is decreased by 1%, what is the new interest?

View solution & Explanation

Correct Answer Rs. 300

Original interest = 3360 - 3000 = 360

Using SI formula:

360 = 3000 R 2 / 100

360 = 60R

R = 6%

New rate = 6% - 1% = 5%

New interest = 3000 5 2 / 100 = 300

So, new interest = Rs. 300

Q11

A man buys a laptop priced at Rs. 20,000. He pays Rs. 5,000 at once and the rest after 12 months on which he is charged a simple interest at the rate of 10% per year. The total amount he pays for the laptop is:

View solution & Explanation

Correct Answer Rs. 21,500

Balance amount = 20000 - 5000 = 15000

Interest on balance for 1 year = 15000 10 1 / 100 = 1500

Amount paid later = 15000 + 1500 = 16500

Total amount paid = 5000 + 16500 = 21500

So, the total amount paid = Rs. 21,500

Q12

A sum of Rs. 2000 was lent partly at 4% and partly at 7% p.a. simple interest. The total interest received after 2 years was Rs. 220. The ratio of the money lent at 4% to that lent at 7% is:

View solution & Explanation

Correct Answer 1:1

Let the amount at 4% = x

Then amount at 7% = 2000 - x

Interest from first part in 2 years = x 4 2 / 100 = 0.08x

Interest from second part in 2 years = (2000 - x) 7 2 / 100 = 0.14(2000 - x)

Total interest = 220

0.08x + 0.14(2000 - x) = 220

0.08x + 280 - 0.14x = 220

280 - 0.06x = 220

280 - 220 = 0.06x

60 = 0.06x

x = 1000

Second part = 2000 - 1000 = 1000

Ratio = 1000 : 1000 = 1 : 1

So, the ratio is 1 : 1

Q13

A sum of Rs. 2500 yields an interest of Rs. 750 at 10% per annum simple interest in how many years?

View solution & Explanation

Correct Answer 3 years

SI = P R T / 100

750 = 2500 10 T / 100

750 = 250T

T = 750/250 T = 3

So, time = 3 years

Q14

A washing machine is available for Rs. 12,000 or Rs. 2,400 down payment, followed by 4 equal monthly instalments. If the rate of interest is 15% p.a. simple interest, calculate the amount of each instalment.

View solution & Explanation

Correct Answer Rs. 2475

Amount left after down payment = 12000 - 2400 = 9600

There are 4 equal monthly instalments.

Average time = 1 + 2 + 3 + 4 / 4 months = 10/4 months = 2.5 months

Interest = 9600 15 2.5 / (100 * 12)

= 9600 15 2.5 / 1200 = 300

Total amount paid in instalments = 9600 + 300 = 9900

Each instalment = 9900/4 = 2475

So, each instalment = Rs. 2475

Q15

In a certain duration of time, a sum becomes 3 times itself at the rate of 4% per annum simple interest. What will be the rate of interest if the same sum becomes 6 times itself in the same duration?

View solution & Explanation

Correct Answer 10%

If the sum becomes 3 times, then interest = 3P - P = 2P

At 4%, this happens in some fixed time.

Now in the same time, sum becomes 6 times.

So interest = 6P - P = 5P

Rate is directly proportional to interest when time is same.

New rate = 4 * 5/2 = 10

So, the new rate = 10%

Q16

If the simple interest on a sum of Rs. P at 4% per annum for five years is thrice the simple interest received on Rs. Q at 6% per annum for two years, then find the relation between P and Q.

View solution & Explanation

Correct Answer P : Q = 9 : 5

Simple interest on P = P 4 5 / 100 = 20P/100

Simple interest on Q = Q 6 2 / 100 = 12Q/100

Given first interest is thrice second interest:

20P/100 = 3 * 12Q/100

20P = 36Q

P/Q = 36/20 = 9/5

So, P : Q = 9 : 5

Q17

What is the present value of Rs. 14,641 received in 2 years, if the interest rate is 20% per year discounted semi-annually?

View solution & Explanation

Correct Answer Rs. 10,000

Semi-annual rate = 20/2 = 10%

Number of half-years in 2 years = 2 * 2 = 4

Present value = 14641/(1.1 1.1 1.1 * 1.1)

1.1 1.1 = 1.21 1.21 1.1 = 1.331 1.331 * 1.1 = 1.4641

Present value = 14641/1.4641 = 10000

So, present value = Rs. 10,000

Q18

A sum of Rs. 20 is lent by a child to his friend to be returned in 11 monthly instalments of Rs. 2 each, the interest being simple. The rate of interest is:

View solution & Explanation

Correct Answer 20%

Total returned = 11 * 2 = 22

Interest = 22 - 20 = 2

The 11 instalments are paid monthly.

Average time = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 / 11 months = 66/11 months = 6 months = 1/2 year

Now,

SI = P R T / 100

2 = 20 R 1/2 / 100

2 = 10R/100

2 = R/10

R = 20

So, the rate of interest = 20%

Q19

A sum of money invested at simple interest becomes 13/10 of itself in 3 years. What is the rate of interest per annum?

View solution & Explanation

Correct Answer 10%

Amount becomes 13/10 of principal.

So, interest = 13/10 - 1 = 3/10 of principal = 30% of principal

This 30% interest is for 3 years.

Rate per year = 30/3 = 10

So, rate of interest = 10% per annum

Q20

At which rate of simple interest does an amount become double in 15 years?

View solution & Explanation

Correct Answer 6 2/3%

For an amount to become double, interest = 100% of principal

Rate = 100/15

= 6.666...

= 6 2/3%

So, the rate of simple interest = 6 2/3%

Successfully you have reached the final question

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