Sophie has $40 in an account. The interest rate is 5% compounded annually. To the nearest cent, how much interest will she earn in 3 years?
The formula to calculate the amount of interest earned over a certain number of years, with interest compounded annually, is:
Interest = Principal x (1 + interest rate)^number of years - Principal
In this case, Sophie's principal is $40, the interest rate is 5%, and she will be earning interest for 3 years.
Plugging these values into the formula:
Interest = $40 x (1 + 0.05)^3 - $40
Interest = $40 x 1.05^3 - $40
Interest = $40 x 1.157625 - $40
Interest ≈ $46.31 - $40
Interest ≈ $6.31
Therefore, Sophie will earn approximately $6.31 in interest over 3 years.