Final answer:
Peter is earning a 6.71% interest rate on his $500 investment over 4.5 years, which is calculated by dividing the total interest earned by the product of the principal amount and the time in years, and then multiplying by 100 to convert it to a percentage.
Step-by-step explanation:
Peter has $500 that he will invest for 4.5 years, and from which he will earn $150.75 in interest. To find out the percent interest he is earning, we can use the simple interest formula, which is Interest = Principal × rate × time. Since we know both the principal amount and the interest earned, we can rearrange the formula to solve for the rate.
First, we'll plug in the values we know:
So, we get $150.75 = $500 × rate × 4.5. To find the rate, we divide both sides by $500 × 4.5:
rate = $150.75 / ($500 × 4.5)
rate = 0.0671 (rounded to four decimal places)
To express the rate as a percentage, we multiply by 100:
Rate = 0.0671 × 100
Rate = 6.71%
Therefore, Peter is earning a 6.71% interest rate on his $500 investment over 4.5 years.