# Compound Interest Quiz Set 008

### Question 1

Rs. 1224 is divided into parts such that the compound amount on first part after 6 years is same as that for the other part after 7 years. What is the first part if the rate of interest in both the cases is 4%?

A

Rs. 624.

B

Rs. 724.

C

Rs. 524.

D

Rs. 824.

Soln.
Ans: a

Let the parts P and (1224 - P). We have P × \$(1 + 4/100)^6\$ = (1224 - P) × \$(1 + 4/100)^7\$. Cancelling, we get P = (1224 - P) × (1 + 4/100). Simplifying, P = \${1224 × (100 + 4)}/(200 + 4)\$, which gives P = Rs. 624.

### Question 2

When a certain amount is invested in a simple interest scheme, it increases by 30% in 3 years. What will be compound interest after 3 years on an amount of Rs. 8000, at the same interest rate, and annual compounding?

A

Rs. 2648.

B

Rs. 2748.

C

Rs. 2548.

D

Rs. 2848.

Soln.
Ans: a

Simple interest on Rs. 100 in 3 years is Rs. 30, so rate is 30/3 = 10%. Compound interest for 3 years would be 8000 × \$(1 + 10/100)^3\$ = 8000 × \$(11/10)^3\$ = \$(8000 × 11 × 11 × 11)/1000\$ = Rs. 10648. Interest = A - P = 10648 - 8000 = Rs. 2648.

### Question 3

What is the amount receivable on Rs. 90000 after 6 months, invested at a rate of 12% compounded quarterly?

A

Rs. 95481.

B

Rs. 95581.

C

Rs. 95381.

D

Rs. 95681.

Soln.
Ans: a

In this case r = \$12/4\$% and n = 2 because compounding is quarterly. So A = 90000 × \$(1 + 3/100)^2\$, which equals 9 × 103 × 103, i.e., Rs. 95481.

### Question 4

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 5

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. 20000.

A

Rs. 8.

B

Rs. 108.

C

Rs. 58.

D

Rs. 208.

Soln.
Ans: a

The simple interest SI = (P × r)/100 = (20000 × 4)/100 = Rs. 800. Compound interest will have half interest rate and n = 2. By shortcut formula, we have CI = \${P × R × (R + 200)}/10000\$ = \${20000 × 2 × (2 + 200)}/10000\$ = Rs. 808. The difference = Rs. 8.