# Compound Interest Quiz Set 015

### Question 1

The compound amount after 2 years on a principal of Rs. P is same as that on a principal of Rs. (404 - P) after 3 years, then what is P if the rate of interest is 2% p.a. compounded yearly?

A

Rs. 204.

B

Rs. 304.

C

Rs. 104.

D

Rs. 404.

Soln.
Ans: a

We have P × $(1 + 2/100)^2$ = (404 - P) × $(1 + 2/100)^3$. Cancelling, we get P = (404 - P) × (1 + 2/100). Simplifying, P = ${404 × (100 + 2)}/(200 + 2)$, which gives P = Rs. 204.

### Question 2

The difference between compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 216. What is the rate p.a. if principal is Rs. 60000?

A

6%.

B

8%.

C

7%.

D

9%.

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 × $√{216/60000}$ = 6%.

### Question 3

An amount P is invested for 1 year @4% p.a. The simple interest is Rs. 4000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 4000.

B

Rs. 4100.

C

Rs. 3900.

D

Rs. 4200.

Soln.
Ans: a

The compound interest and simple interest are exactly same for a period of 1 year if P and r are always same.

### Question 4

What is the difference between the simple interest and compound interest at the rate of 4% for 1 year? The compounding is half-yearly, and the principal is Rs. 50000.

A

Rs. 20.

B

Rs. 120.

C

Rs. 70.

D

Rs. 220.

Soln.
Ans: a

The simple interest SI = (P × r)/100 = (50000 × 4)/100 = Rs. 2000. Compound interest will have half interest rate and n = 2. By shortcut formula, we have CI = ${P × R × (R + 200)}/10000$ = ${50000 × 2 × (2 + 200)}/10000$ = Rs. 2020. The difference = Rs. 20.

### Question 5

The difference in compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 512. What is the principal amount if the rate is 8% p.a.?

A

Rs. 80000.

B

Rs. 90000.

C

Rs. 70000.

D

Rs. 100000.

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 = $(Difference × 10000)/(rate × rate)$ = $(512 × 10000)/(8 × 8)$ = Rs. 80000.