# Compound Interest Quiz Set 002

### Question 1

An amount P is invested for 2 years @6% p.a. The simple interest is Rs. 7000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 7210.

B

Rs. 7310.

C

Rs. 7110.

D

Rs. 7410.

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\$ = \${7000 × (6 + 200)}/200\$ = Rs. 7210.

### Question 2

An interest rate of 18% compounded half-annually is offered by a bank. An account holder deposits Rs. 60000 in the bank under this scheme. After six months he again deposits Rs 60000. What is the total amount that he will get after 1 year?

A

Rs. 136686.

B

Rs. 154444.

C

Rs. 154244.

D

Rs. 154544.

Soln.
Ans: a

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × \$((1 + r/100)^2 + (1 + r/100))\$ = \$P/10000\$ × \$((100 + r)^2 + 100(100 + r))\$ = \$P/10000 × (100 + r)\$ × \$(100 + r + 100)\$ which equals \${P × (100 + r) × (200 + r)}/10000.\$ Putting r = 9 and P = 60000 and cancelling 10000, we get 6 × 109 × 209 = Rs. 136686. Please note that the rate of interest will be 1/2 because the compounding is half yearly.

### Question 3

A bank offers an interest rate of 9% compounded annually. Initially I deposit Rs. 20000 in the bank under this scheme. After 1 year I again deposit Rs 20000. What is the total amount that I will get after 2 years?

A

Rs. 45562.

B

Rs. 45662.

C

Rs. 45462.

D

Rs. 45762.

Soln.
Ans: a

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × \$((1 + r/100)^2 + (1 + r/100))\$ = \$P/10000\$ × \$((100 + r)^2 + 100(100 + r))\$ = \$P/10000 × (100 + r)\$ × \$(100 + r + 100)\$ which equals \${P × (100 + r) × (200 + r)}/10000.\$ Putting r = 9 and P = 20000 and cancelling 10000, we get 2 × 109 × 209 = Rs. 45562.

### Question 4

The amount of Rs. 2000000 earns an interest of Rs. 185454 @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 2000000 + 185454. So 2185454 = 2000000 × \$(103/100)^n\$. So \$2185454/2000000\$ = \$(103/100)^n\$, which can be put in the form \$(103/100)^3\$ = \$(103/100)^3\$, so n = 3 years.

### Question 5

What is the amount receivable on Rs. 3000000 after 9 months, invested at a rate of 16% compounded quarterly?

A

Rs. 3374592.

B

Rs. 3374692.

C

Rs. 3374492.

D

Rs. 3374792.

Soln.
Ans: a

In this case r = \$16/4\$% and n = 3 because compounding is quarterly, and in 9 months there are three quarters. So A = 3000000 × \$(1 + 4/100)^3\$, which equals 3 × 104 × 104 × 104, i.e., Rs. 3374592.