Problem 11 - Entrance Test

The difference in amounts after 7 years and 5 years is the interest earned in 2 years, which is $2940 - $2700 = $240. This interest is for 2 years on the principal amount that grew to $2700 in 5 years. To find the annual rate of interest, first, find the interest for one year, which is $240 / 2 = $120 per year. The principal amount after 5 years is $2700, so the interest rate per year is $120 / $2700 * 100. However, to simplify, the formula for simple interest is I = PRT, where I is the interest, P is the principal, R is the rate of interest, and T is the time. Given the interest for 2 years is $240, we find the principal at the start of the 5-year period by subtracting the interest for 5 years (which we don't directly have) from $2700. But knowing the interest for the last 2 of those 5 years is $240, we can set up a relation based on rates. The interest rate can also be found by considering the total growth over the total period but requires an understanding that the $240 interest for 2 years can help derive the rate over the principal at that time. Using the formula A = P(1 + rt) and given A = $2940, and at 5 years it's $2700, with a difference of $240 over 2 years, suggests calculating back to find the principal and then applying. However, a straightforward calculation from given data directly to the rate involves recognizing the growth from $2700 to $2940 over 2 years is $240, and thus applying the formula for interest rate, where $240 = P * r * 2, but we recognize P here should be the amount at the start of the period for which we're considering the interest, leading to a simplification in thought process focusing on the effective interest and the resulting amount.