Now that Jennifer is in middle school, her parents have decided that they really must start saving for her college education. They have $10,000 to invest right now. Furthermore, they plan to save another $4,000 each year until Jennifer starts college five years from now. They plan to split their investment evenly between a stock fund and a bond fund. Historically, the stock fund has had an average annual return of 8 percent with a standard deviation of 6 percent. The bond fund has had an average annual return of 4 percent with a standard deviation of 3 percent. (Assume a normal distribution for both.)
Assume that the initial investment ($10,000) is made right now (year 0) and is split evenly between the two funds (i.e., $5,000 in each fund). The returns of each fund are allowed to accumulate (i.e., are reinvested) in the same fund and no redistribution will be done before Jennifer starts college. Furthermore, four additional investments of $4,000 will be made and split evenly between both funds ($2,000 each) at the end of year 1, year 2, year 3, and year 4, plus another $4,000 of savings will be available at the end of year 5, just in time for Jennifer to begin college. Use a 1000-trial ASPE simulation to estimate each of the following.
(a) What will be the expected value (mean) of the college fund at the end of year 5?
(b) What will be the standard deviation of the college fund at the end of year 5?
(c) What is the probability that the college fund at the end of year 5 will be at least $35,000?
(d) What is the probability that the college fund at the end of year 5 will be at least $40,000?