# Compound Interest Quiz Set 013

### Question 1

What is the difference in compound interest and simple interest on an amount of Rs. 90000 for a period of 2 years if the rate is 2% p.a. compounded annually?

A

Rs. 36.

B

Rs. 136.

C

Rs. 86.

D

Rs. 236.

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 $(90000 × 2^2)/10000$ = Rs. 36.

### Question 2

What is the amount receivable on Rs. 40000 after 6 months, invested at a rate of 28% compounded quarterly?

A

Rs. 45796.

B

Rs. 45896.

C

Rs. 45696.

D

Rs. 45996.

Soln.
Ans: a

In this case r = $28/4$% and n = 2 because compounding is quarterly. So A = 40000 × $(1 + 7/100)^2$, which equals 4 × 107 × 107, i.e., Rs. 45796.

### Question 3

The amount of Rs. 3000000 earns an interest of Rs. 278181 @3% compounded annually. What is the investment period in years?

A

3 years.

B

2 years.

C

1 year.

D

1/2 year.

Soln.
Ans: a

The amount is 3000000 + 278181. So 3278181 = 3000000 × $(103/100)^n$. So $3278181/3000000$ = $(103/100)^n$, which can be put in the form $(103/100)^3$ = $(103/100)^3$, so n = 3 years.

### Question 4

The interest earned by an amount of Rs. 40000 @5% compounded annually is Rs. 4100. 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 40000 + 4100. So 44100 = 40000 × $(105/100)^n$. So $44100/40000$ = $(105/100)^n$, which can be put in the form $(105/100)^2$ = $(105/100)^n$, so n = 2 years.

### Question 5

The difference between compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 175. What is the rate p.a. if principal is Rs. 70000?

A

5%.

B

7%.

C

6%.

D

8%.

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 × $√{175/70000}$ = 5%. 