# Compound Interest Quiz Set 005

### Question 1

How much interest does an amount of Rs. 1000000 earn @4% compounded annually for 3 years?

A

Rs. 124864.

B

Rs. 124964.

C

Rs. 124764.

D

Rs. 125064.

Soln.
Ans: a

Amount A = 1000000 × $(1 + 4/100)^3$, which equals 1000000 × $104/100$ × $104/100$ × $104/100$ = 1 × 104 × 104 × 104 = Rs. 1124864. So interest = A - P = 1124864 - 1000000 = Rs. 124864.

### Question 2

The difference in compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 54. What is the principal amount if the rate is 3% p.a.?

A

Rs. 60000.

B

Rs. 70000.

C

Rs. 50000.

D

Rs. 80000.

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 = $(Difference × 10000)/(rate × rate)$ = $(54 × 10000)/(3 × 3)$ = Rs. 60000.

### Question 3

An amount P is invested for 2 years @6% p.a. The simple interest is Rs. 6000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 6180.

B

Rs. 6280.

C

Rs. 6080.

D

Rs. 6380.

Soln.
Ans: a

Let SI, P, r, t have usual meanings. Then, for 2 years, SI = (P × r × 2)/100. So P = $(50 × SI)/r$. The compound interest for 2 years by shortcut formula is ${P × r × (200 + r)}/10000$. Putting P here, it becomes, ${{(50 × SI)/r} × r × (200 + r)}/10000$ = ${SI × (r + 200)}/200$ = ${6000 × (6 + 200)}/200$ = Rs. 6180.

### Question 4

An amount P is invested for 1 year @3% p.a. The simple interest is Rs. 6000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 6000.

B

Rs. 6100.

C

Rs. 5900.

D

Rs. 6200.

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 5

The difference in compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 98. What is the principal amount if the rate is 7% p.a.?

A

Rs. 20000.

B

Rs. 30000.

C

Rs. 25000.

D

Rs. 40000.

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 = $(Difference × 10000)/(rate × rate)$ = $(98 × 10000)/(7 × 7)$ = Rs. 20000. 