# Compound Interest Quiz Set 006

### Question 1

Rs. 412 is divided into parts such that the compound amount on first part after 8 years is same as that for the other part after 9 years. What is the first part if the rate of interest in both the cases is 6%?

A

Rs. 212.

B

Rs. 312.

C

Rs. 112.

D

Rs. 412.

Soln.
Ans: a

Let the parts P and (412 - P). We have P × \$(1 + 6/100)^8\$ = (412 - P) × \$(1 + 6/100)^9\$. Cancelling, we get P = (412 - P) × (1 + 6/100). Simplifying, P = \${412 × (100 + 6)}/(200 + 6)\$, which gives P = Rs. 212.

### Question 2

What is the amount receivable on Rs. 2000000 after 9 months, invested at a rate of 24% compounded quarterly?

A

Rs. 2382032.

B

Rs. 2382132.

C

Rs. 2381932.

D

Rs. 2382232.

Soln.
Ans: a

In this case r = \$24/4\$% and n = 3 because compounding is quarterly, and in 9 months there are three quarters. So A = 2000000 × \$(1 + 6/100)^3\$, which equals 2 × 106 × 106 × 106, i.e., Rs. 2382032.

### Question 3

When a certain amount is invested in a simple interest scheme, it increases by 50% in 5 years. What will be compound interest after 3 years on an amount of Rs. 3000, at the same interest rate, and annual compounding?

A

Rs. 993.

B

Rs. 1093.

C

Rs. 893.

D

Rs. 1193.

Soln.
Ans: a

Simple interest on Rs. 100 in 5 years is Rs. 50, so rate is 50/5 = 10%. Compound interest for 3 years would be 3000 × \$(1 + 10/100)^3\$ = 3000 × \$(11/10)^3\$ = \$(3000 × 11 × 11 × 11)/1000\$ = Rs. 3993. Interest = A - P = 3993 - 3000 = Rs. 993.

### Question 4

An amount P is invested for 1 year @4% p.a. The simple interest is Rs. 3000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 3000.

B

Rs. 3100.

C

Rs. 2900.

D

Rs. 3200.

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

When a certain amount is invested in a simple interest scheme, it increases by 60% in 6 years. What will be compound interest after 3 years on an amount of Rs. 6000, at the same interest rate, and annual compounding?

A

Rs. 1986.

B

Rs. 2086.

C

Rs. 1886.

D

Rs. 2186.

Soln.
Ans: a

Simple interest on Rs. 100 in 6 years is Rs. 60, so rate is 60/6 = 10%. Compound interest for 3 years would be 6000 × \$(1 + 10/100)^3\$ = 6000 × \$(11/10)^3\$ = \$(6000 × 11 × 11 × 11)/1000\$ = Rs. 7986. Interest = A - P = 7986 - 6000 = Rs. 1986.