(Future value of an annuity) Let's say you deposited $180,000 in a 529 plan (a tax advantaged college savings plan) hoping to have $420,000 available 15 years later when your first child starts college. However, you didn't invest very well, and 3 years later the account balance dropped to $160,000. 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 3 years ago? b. With only $160,000 in the fund and 12 years remaining until your first child starts college, what annual rate of return would the fund have to make t reach your $420,000 goal if you add nothing to the account? c. Shocked by your experience of the past 3 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 12 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 which is compounded monthly. You decide to transfer the $160,000 to this new fund and make the necessary monthly deposits. How large of a monthly deposit must you make into this new fund? d. After seeing how large the monthly deposit would be (in part c of this problem), you decide to invest the $160,000 today and $450 at the end of each month for the next 12 years into a fund consisting of 50 percent stock and 50 percent bonds and hope for the best. What APR would the fund have to earn in order to reach your $420,000 goal? a. If you invested $180,000 into a fund 3 years ago and hoped to have $420,000 available 15 years later when your first child starts college, what was the original annual rate of return needed to reach your goal when you started the fund 3 years ago? 1% (Round to two decimal places.) b. Now with only $160,000 in the fund and 12 years remaining until your first child starts college, what annual rate of return would the fund have to earn to reach your $420,000 goal if you add nothing to the account? % (Round to two decimal places.) c. If you decide to transfer the $160,000 to a new fund that promises to pay a guaranteed return of 6 percent compounded monthly and make the necessary end-of-the-month deposits, how large of a monthly deposit must you make into this new fund to meet your $420,000 goal in 12 years? (Round to the nearest cent.) d. Now you decide to invest the $160,000 today and $450 at the end of each month for the next 12 years into a fund consisting of 50 percent stock and 50 percent bonds and hope for the best. What annual rate of return would the fund have earn in order to reach your $420,000 goal? % (Round to two decimal places.)
