# Compound Interest Quiz Set 020

### Question 1

The compound amount after 3 years on a principal of Rs. x is same as that on a principal of Rs. (1030 - x) after 4 years, then what is x if the rate of interest is 6% p.a. compounded yearly?

A

Rs. 530.

B

Rs. 630.

C

Rs. 430.

D

Rs. 730.

Soln.
Ans: a

We have x × $(1 + 6/100)^3$ = (1030 - x) × $(1 + 6/100)^4$. Cancelling, we get x = (1030 - x) × (1 + 6/100). Simplifying, x = ${1030 × (100 + 6)}/(200 + 6)$, which gives x = Rs. 530.

### Question 2

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 3

What is the difference in compound interest and simple interest on an amount of Rs. 20000 for a period of 2 years if the rate is 8% p.a. compounded annually?

A

Rs. 128.

B

Rs. 228.

C

Rs. 178.

D

Rs. 328.

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 $(20000 × 8^2)/10000$ = Rs. 128.

### Question 4

The difference between compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 8. What is the rate p.a. if principal is Rs. 20000?

A

2%.

B

4%.

C

3%.

D

5%.

Soln.
Ans: a

If d is the difference, r is the rate and P is the principal, then the shortcut formula for the difference between compound and simple interest over a period of 2 years is d = P × $(r/100)^2$. So rate = 100 × $√{d/P}$ = 100 × $√{8/20000}$ = 2%.

### Question 5

What is the amount receivable on Rs. 20000 after 6 months, invested at a rate of 24% compounded quarterly?

A

Rs. 22472.

B

Rs. 22572.

C

Rs. 22372.

D

Rs. 22672.

Soln.
Ans: a

In this case r = $24/4$% and n = 2 because compounding is quarterly. So A = 20000 × $(1 + 6/100)^2$, which equals 2 × 106 × 106, i.e., Rs. 22472. 