# Compound Interest Quiz Set 019

### Question 1

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 2

How much interest does an amount of Rs. 3000000 earn @8% compounded annually for 3 years?

A

Rs. 779136.

B

Rs. 779236.

C

Rs. 779036.

D

Rs. 779336.

Soln.
Ans: a

Amount A = 3000000 × $(1 + 8/100)^3$, which equals 3000000 × $108/100$ × $108/100$ × $108/100$ = 3 × 108 × 108 × 108 = Rs. 3779136. So interest = A - P = 3779136 - 3000000 = Rs. 779136.

### Question 3

The compound amount after 3 years on a principal of Rs. x is same as that on a principal of Rs. (621 - x) after 4 years, then what is x if the rate of interest is 7% p.a. compounded yearly?

A

Rs. 321.

B

Rs. 421.

C

Rs. 221.

D

Rs. 521.

Soln.
Ans: a

We have x × $(1 + 7/100)^3$ = (621 - x) × $(1 + 7/100)^4$. Cancelling, we get x = (621 - x) × (1 + 7/100). Simplifying, x = ${621 × (100 + 7)}/(200 + 7)$, which gives x = Rs. 321.

### Question 4

The interest earned by an amount of Rs. 20000 @5% compounded annually is Rs. 2050. 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 20000 + 2050. So 22050 = 20000 × $(105/100)^n$. So $22050/20000$ = $(105/100)^n$, which can be put in the form $(105/100)^2$ = $(105/100)^n$, so n = 2 years.

### Question 5

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.