GMAT Quant Practice | Simple Interest Q18

The given question is a GMAT 550-600 level problem solving question from the topic Simple Interest. It tests the concept of finding principal invested and rate of interest based on data about interest earned.

Question 18: 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%

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Video Explanation

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Explanatory Answer | GMAT Simple Interest

Step 1 : Compute principal invested

Concept: Simple interest earned remains same year after year.

Initial amount invested = P
Value of investment (Amount) at the end of year 3 = $300
Value of investment (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{\text{100 }}{\text{5}}) = $20.
Therefore, interest earned for 3 years = 3 × 20 = $60.
Hence, initial amount invested P = Amount after 3 years - interest for 3 years
P = $300 − $60 = $240

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Step 2 : Find the rate of interest

Simple interest = \\frac{\text{Principal × number of years × rate of interest}}{\text{100}})
Simple interest = $20, Principal P = $240, n = 1 year.
Rate of interest r = \\frac{\text{20}}{\text{240}}) × 100 = 8.33%
Rate of interest is 8.33%

Choice E is the correct answer.