# GMAT Quant : Simple & Compound Interest

Concept: Finding the number of years of a Simple interest.

The question given below is a problem solving question in Simple Interest. A relatively easy question.

#### Question: 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

Video explanation will be added soon

Simple interest is calculated by \\frac{Principal * number of years * rate of interest}{100}) …………1

In this question, principal is not given. However, for any assumed principal, the number of years is going to remain the same because the amount is expressed as ‘x’ times the principal – 4 times in this case.

Amount = Principal + Simple Interest.

Let us assume that Braun invested $100. Then, at the end of 'n' years he would have got$400.

Therefore, the Simple Interest earned = 400 - 100 = $300. Substitute values of simple interest, principal and rate in equation 1. 300 = \\frac{100 * n * 8}{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 original investment made. ##### Alternative Method: If you invest at 8% p.a. simple interest$100 will earn $100 interest in 12.5 years. All you must do to find the number of years is substitute principal = 100, interest = 100 and r = 8% in the simple interest formula. 100 = \\frac{100 * n * 8}{100}) So, n = \\frac{100}{8}) = 12.5 years.$100 earned $300 interest to become$400.

To earn $100 interest it took 12.5 years. It will take 3 * 12.5 = 37.5 years to earn$300 interest.

Choice D is the correct answer.

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