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### 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?

### 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?

### 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 2017-04-07.