# Compound Interest Quiz Set 020

### Question 1

The difference in compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 343. What is the principal amount if the rate is 7% 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 = $(Difference × 10000)/(rate × rate)$ = $(343 × 10000)/(7 × 7)$ = Rs. 70000.

### Question 2

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 3

What is compound interest on Rs. 70000 after 2 years, invested at a rate of 3% compounded annually?

A

Rs. 4263.

B

Rs. 4363.

C

Rs. 4163.

D

Rs. 4463.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting P = 70000, r = 3, we get ${70000 × 3 × (3 + 200)}/10000$ = Rs. 4263.

### Question 4

What is the amount receivable on Rs. 80000 after 6 months, invested at a rate of 8% compounded quarterly?

A

Rs. 83232.

B

Rs. 83332.

C

Rs. 83132.

D

Rs. 83432.

Soln.
Ans: a

In this case r = $8/4$% and n = 2 because compounding is quarterly. So A = 80000 × $(1 + 2/100)^2$, which equals 8 × 102 × 102, i.e., Rs. 83232.

### Question 5

What is compound interest on Rs. 90000 after 2 years, invested at a rate of 3% compounded annually?

A

Rs. 5481.

B

Rs. 5581.

C

Rs. 5381.

D

Rs. 5681.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting P = 90000, r = 3, we get ${90000 × 3 × (3 + 200)}/10000$ = Rs. 5481.