# Compound Interest Quiz Set 011

### Question 1

How much interest does an amount of Rs. 8000000 earn @3% compounded annually for 3 years?

A

Rs. 741816.

B

Rs. 741916.

C

Rs. 741716.

D

Rs. 742016.

Soln.
Ans: a

Amount A = 8000000 × \$(1 + 3/100)^3\$, which equals 8000000 × \$103/100\$ × \$103/100\$ × \$103/100\$ = 8 × 103 × 103 × 103 = Rs. 8741816. So interest = A - P = 8741816 - 8000000 = Rs. 741816.

### Question 2

What is the amount receivable on Rs. 2000000 after 9 months, invested at a rate of 28% compounded quarterly?

A

Rs. 2450086.

B

Rs. 2450186.

C

Rs. 2449986.

D

Rs. 2450286.

Soln.
Ans: a

In this case r = \$28/4\$% and n = 3 because compounding is quarterly, and in 9 months there are three quarters. So A = 2000000 × \$(1 + 7/100)^3\$, which equals 2 × 107 × 107 × 107, i.e., Rs. 2450086.

### Question 3

The interest earned by an amount of Rs. 90000 @5% compounded annually is Rs. 9225. What is the period in years?

A

2 years.

B

3 years.

C

1 year.

D

1/2 year.

Soln.
Ans: a

The amount is 90000 + 9225. So 99225 = 90000 × \$(105/100)^n\$. So \$99225/90000\$ = \$(105/100)^n\$, which can be put in the form \$(105/100)^2\$ = \$(105/100)^n\$, so n = 2 years.

### Question 4

The amount of Rs. 8000000 earns an interest of Rs. 741816 @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 8000000 + 741816. So 8741816 = 8000000 × \$(103/100)^n\$. So \$8741816/8000000\$ = \$(103/100)^n\$, which can be put in the form \$(103/100)^3\$ = \$(103/100)^3\$, so n = 3 years.

### Question 5

A bank offers an interest rate of 5% compounded annually. Initially I deposit Rs. 50000 in the bank under this scheme. After 1 year I again deposit Rs 50000. What is the total amount that I will get after 2 years?

A

Rs. 107625.

B

Rs. 107725.

C

Rs. 107525.

D

Rs. 107825.

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 = 5 and P = 50000 and cancelling 10000, we get 5 × 105 × 205 = Rs. 107625. 