A certain sum of money amounts to $660 in 3 years and $726 in 5 years when invested at a certain rate of interest compounded annually. What is the rate of interest?
Correct: C
The difference in amounts after 5 years and 3 years is $726 - $660 = $66, which is the interest earned in 2 years. Since the interest is compounded annually, we can use the formula A = P(1 + r)^n, where A is the amount after n years, P is the principal amount, r is the rate of interest, and n is the number of years. However, to simplify the calculation and directly address the rate of interest: The interest earned in the last two years ($66) is the interest on the amount that was $660 at the end of year 3. The annual interest can be approximated as $66 / 2 = $33 per year. As a percentage of $660 (the principal after 3 years), this is (33 / 660) * 100, which is roughly 5%. The exact calculation should involve using the formula for compound interest to set up equations based on the given amounts and solving for r, but this approach simplifies to understanding the increase.