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Simple and Compound Interest - December 18, 2003
The GMAT Sample Math question for the day is from the topic Simple and Compound 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?
A. 12%
B. 12.5%
C. 6.67%
D. 6.25%
E. 8.33%
The correct choice is (E) and the correct answer is 8.33%.
Explanatory Answer
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
As the simple interest earned for a period of 5 years is $ 100, interest earned per year = $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 =  =  = 8.33%
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