# Compound Interest Quiz Set 002

### Question 1

An interest rate of 18% compounded half-annually is offered by a bank. An account holder deposits Rs. 60000 in the bank under this scheme. After six months he again deposits Rs 60000. What is the total amount that he will get after 1 year?

A

Rs. 136686.

B

Rs. 154444.

C

Rs. 154244.

D

Rs. 154544.

Soln.
Ans: a

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × $((1 + r/100)^2 + (1 + r/100))$ = $P/10000$ × $((100 + r)^2 + 100(100 + r))$ = $P/10000 × (100 + r)$ × $(100 + r + 100)$ which equals ${P × (100 + r) × (200 + r)}/10000.$ Putting r = 9 and P = 60000 and cancelling 10000, we get 6 × 109 × 209 = Rs. 136686. Please note that the rate of interest will be 1/2 because the compounding is half yearly.

### Question 2

What is the amount receivable on Rs. 60000 after 6 months, invested at a rate of 20% compounded quarterly?

A

Rs. 66150.

B

Rs. 66250.

C

Rs. 66050.

D

Rs. 66350.

Soln.
Ans: a

In this case r = $20/4$% and n = 2 because compounding is quarterly. So A = 60000 × $(1 + 5/100)^2$, which equals 6 × 105 × 105, i.e., Rs. 66150.

### Question 3

The difference in compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 54. What is the principal amount if the rate is 3% p.a.?

A

Rs. 60000.

B

Rs. 70000.

C

Rs. 50000.

D

Rs. 80000.

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 = $(Difference × 10000)/(rate × rate)$ = $(54 × 10000)/(3 × 3)$ = Rs. 60000.

### Question 4

What is the difference in compound interest and simple interest on an amount of Rs. 30000 for a period of 2 years if the rate is 5% p.a. compounded annually?

A

Rs. 75.

B

Rs. 175.

C

Rs. 125.

D

Rs. 275.

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 $(30000 × 5^2)/10000$ = Rs. 75.

### Question 5

How much interest does an amount of Rs. 50000 earn @4% compounded annually for 2 years?

A

Rs. 4080.

B

Rs. 4180.

C

Rs. 3980.

D

Rs. 4280.

Soln.
Ans: a

Amount A = 50000 × $(1 + 4/100)^2$, which equals 50000 × $104/100$ × $104/100$ = 5 × 104 × 104 = Rs. 54080. So interest = A - P = 54080 - 50000 = Rs. 4080.