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?

- 12%
- 12.5%
- 6.67%
- 6.25%
- 8.33%

@ INR

**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

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%**

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