# GMAT Quant Practice | Simple Interest Q18

#### Simple Interest | Word Problem

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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### 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 #### 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. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch Dec 14, 2023 ## Additional Practice Questions in Ratio Proportion, Mixtures, Percents, Fractions, Profits, and Interest ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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