GMAT Math Questions | Simple Interest Q15

The given question is a GMAT 550 level problem solving question from the topic Simple Interest. This GMAT sample question tests the concept of computing the number of years for which an investment was made.

Question 15: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 4 times his original investment. What is the value of n?

1. 50 years
2. 25 years
3. 12 years 6 months
4. 37 years 6 months
5. 40 years

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Video Explanation

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Explanatory Answer | GMAT Simple Interest

Step 1 : Assume initial investment (Principal) and compute final value (amount) after n years

Simple interest = \\frac{\text{Principal × number of years × rate of interest}}{\text{100}}) . . . . (1)

For any assumed principal, the number of years is going to remain the same because the amount is expressed as ‘x’ times the principal i.e., 4 times in this case.
Let us assume the initial investment (principal) by Braun to be $100.
Amount = 4 × Principal = $400
Amount = Principal + Simple Interest
Therefore, the Simple Interest earned = 400 - 100 = $300.

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Step 2 : Find the number of years n

Substitute assumed value of principal and the corresponding interest earned, and rate of interest in equation 1.
300 = \\frac{\text{100 × n × 8}}{\text{100}})
Or 8n = 300
Or n = 37.5 years
Any amount, when invested for 37.5 years at 8% per annum simple interest would become 4 times the initial value.

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Alternative Method:

Find the number of years required to double the initial amount (principal).
When the initial investment doubles, the interest earned is the same as the initial investment (principal).
So, if principal = 100, interest earned = 100 and r = 8%.
100 = \\frac{\text{100 × n × 8}}{\text{100}})
So, n =\\frac{\text{100 }}{\text{8}})= 12.5 years.

Initial investment of $100 becomes $400 after earning an interest of $300.
To earn $100 interest it took 12.5 years. Hence, it will take 3 × 12.5 = 37.5 years to earn $300 interest.

Choice D is the correct answer.