(Calculating the future value of an annuity) Let’s say you deposited $160,000 in a 529 plan (a tax-advantaged college savings plan), hoping to have $420,000 available 12 years later when your first child starts college. However, you didn’t invest very well, and two years later the account’s balance dropped to $140,000. Let’s look at what you need to do to get the college savings plan back on track.

a. What was the original annual rate of return needed to reach your goal when you started the fund two years ago?

b. With only $140,000 in the fund and 10 years remaining until your first child starts college, what annual rate of return will the fund have to make to reach your

$420,000 goal if you add nothing to the account?

c. Shocked by your experience of the past two years, you feel the college fund has invested too much in stocks, and you want a low-risk fund in order to ensure you have the necessary $420,000 in 10 years. You are willing to make end-of-the-month deposits to the fund as well. You find you can get a fund that promises to pay a guaranteed annual return of 6 percent that is compounded monthly. You decide to transfer the $140,000 to this new fund and make the necessary monthly deposits.

How large of a monthly deposit must you make in this new fund each month?

d. After seeing how large the monthly deposit has to be (in part c of this problem), you decide to invest the $140,000 today and $500 at the end of each month for the next 10 years in a fund consisting of 50 percent stock and 50 percent bonds and to hope for the best. What APR will the fund have to earn in order to reach your

$420,000 goal?