Simple and Compound Interest Set 1
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.
Q1.A scooter worth Rs. 50,000 depreciates at 10% per annum. Find its value after two years.
View Solution & Explanation
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
Q2.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
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
Q3. 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
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
Q4.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
Simple interest formula:
SI = P R T / 100
144 = 800 6 T / 100
144 = 48T
T = 144/48 T = 3
So, time = 3 years
Q5.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
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
Q6.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
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%
Q7.In how many years will a sum of money double itself at 12.5% per annum simple interest?
View Solution & Explanation
To double, interest = principal
So, SI = 100% of principal
Time = 100/12.5 = 8
So, the money will double in 8 years
Q8.If a sum doubles in 20 years, how much will it be in 10 years?
View Solution & Explanation
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
Q9.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
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
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
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
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
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
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
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
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
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
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
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
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%
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