Final answer:
To cover the cost of a child's college education in 16 years at a total cost of $380,000 starting with an investment of $62,000, an annual rate of interest of approximately 7.46% is required.
Step-by-step explanation:
To find the annual rate of interest necessary to grow an investment of $62,000 to $380,000 in 16 years, we can use the formula for compound interest. The formula we need is the Future Value formula for compound interest which is FV = PV(1 + r)^n, where FV is the future value of the investment, PV is the present value, r is the annual interest rate, and n is the number of years.
Here, the future value (FV) is $380,000, the present value (PV) is $62,000, and the number of years (n) is 16. We're solving for the rate (r).
By rearranging the formula to solve for r, we have r = ((FV/PV)^(1/n)) - 1. Plugging in the numbers we get r = (($380,000 / $62,000)^(1/16)) - 1.
After calculating the result, we find that the annual rate of interest required is approximately r = 0.0746 or 7.46% when rounded to two decimal places.