# Compound Interest Quiz Set 017

### Question 1

An amount P is invested for 1 year @6% p.a. The simple interest is Rs. 4000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 4000.

B

Rs. 4100.

C

Rs. 3900.

D

Rs. 4200.

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 2

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 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. 2000, at the same interest rate, and annual compounding?

A

Rs. 662.

B

Rs. 762.

C

Rs. 562.

D

Rs. 862.

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 2000 × \$(1 + 10/100)^3\$ = 2000 × \$(11/10)^3\$ = \$(2000 × 11 × 11 × 11)/1000\$ = Rs. 2662. Interest = A - P = 2662 - 2000 = Rs. 662.

### Question 4

The compound amount after 3 years on a principal of Rs. x is same as that on a principal of Rs. (621 - x) after 4 years, then what is x if the rate of interest is 7% p.a. compounded yearly?

A

Rs. 321.

B

Rs. 421.

C

Rs. 221.

D

Rs. 521.

Soln.
Ans: a

We have x × \$(1 + 7/100)^3\$ = (621 - x) × \$(1 + 7/100)^4\$. Cancelling, we get x = (621 - x) × (1 + 7/100). Simplifying, x = \${621 × (100 + 7)}/(200 + 7)\$, which gives x = Rs. 321.

### Question 5

An interest rate of 10% compounded half-annually is offered by a bank. An account holder deposits Rs. 30000 in the bank under this scheme. After six months he again deposits Rs 30000. What is the total amount that he will get after 1 year?

A

Rs. 64575.

B

Rs. 69400.

C

Rs. 69200.

D

Rs. 69500.

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 = 30000 and cancelling 10000, we get 3 × 105 × 205 = Rs. 64575. Please note that the rate of interest will be 1/2 because the compounding is half yearly.

This Blog Post/Article "Compound Interest Quiz Set 017" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer