Compound Interest Quiz Set 005

Question 1

The interest earned by an amount of Rs. 90000 @5% compounded annually is Rs. 9225. What is the period in years?

A

2 years.

B

3 years.

C

1 year.

D

1/2 year.

Soln.
Ans: a

The amount is 90000 + 9225. So 99225 = 90000 × $(105/100)^n$. So $99225/90000$ = $(105/100)^n$, which can be put in the form $(105/100)^2$ = $(105/100)^n$, so n = 2 years.

Question 2

What is the difference in compound interest and simple interest on an amount of Rs. 60000 for a period of 2 years if the rate is 2% p.a. compounded annually?

A

Rs. 24.

B

Rs. 124.

C

Rs. 74.

D

Rs. 224.

Soln.
Ans: a

The shortcut formula for the difference between compound and simple interest over a period of 2 years is $Difference = Principal × (\text"rate"/100)^2$, which equals $(60000 × 2^2)/10000$ = Rs. 24.

Question 3

How much interest does an amount of Rs. 9000000 earn @5% compounded annually for 3 years?

A

Rs. 1418625.

B

Rs. 1418725.

C

Rs. 1418525.

D

Rs. 1418825.

Soln.
Ans: a

Amount A = 9000000 × $(1 + 5/100)^3$, which equals 9000000 × $105/100$ × $105/100$ × $105/100$ = 9 × 105 × 105 × 105 = Rs. 10418625. So interest = A - P = 10418625 - 9000000 = Rs. 1418625.

Question 4

The difference in compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 252. What is the principal amount if the rate is 6% p.a.?

A

Rs. 70000.

B

Rs. 80000.

C

Rs. 60000.

D

Rs. 90000.

Soln.
Ans: a

The shortcut formula for the difference between compound and simple interest over a period of 2 years is $Difference = Principal × (\text"rate"/100)^2$. So Principal = $(Difference × 10000)/(rate × rate)$ = $(252 × 10000)/(6 × 6)$ = Rs. 70000.

Question 5

An amount P is invested for 1 year @4% p.a. The simple interest is Rs. 3000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 3000.

B

Rs. 3100.

C

Rs. 2900.

D

Rs. 3200.

Soln.
Ans: a

The compound interest and simple interest are exactly same for a period of 1 year if P and r are always same.