# GMAT Quant : Simple & Compound Interest

Concept: Computing Rate of interest.

The question given below is a problem solving question in Simple Interest in finding the rate of interest.

#### Question: Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to$ 400 at the end of another 5 years. What was the rate of interest in which he invested his sum?

1. 12%
2. 12.5%
3. 6.67%
4. 6.25%
5. 8.33%

Video explanation will be added soon

This problem is also similar to question three: We need to figured out the interest earned between years 3 and 8 and use that to calculate interest earned each year.

Initial amount invested = $X Amount at the end of year 3 =$ 300

Amount at the end of year 8 (another 5 years) = $400 Therefore, the interest earned for the 5 year period between the 3rd year and 8th year =$400 - $300 =$100

So, interest earned per year = $\frac{100}{5}$ = $20. Therefore, interest earned for 3 years = 3 * 20 =$ 60.

Hence, initial amount invested X = Amount after 3 years - interest for 3 years

= 300 - 60 = \$ 240.

Rate of interest = $\frac{interest per year}{principal invested}$ * 100 = $\frac{20}{240}$ * 100 = 8.33%

Choice E is the correct answer.

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