Future value of an annuity) Let's say you deposited 5160,000 in a 529 plan (a tax advantaged college savings plan) hoping to have s420,000 available 12 years ater when your first child starts college. However, you didn't invest very well and 2 years later the account balance dropped to $140,000 Let's look at what you need to do to get the college savings plan back on track. 9. What was the original annual rate of retum needed to reach your goal when you started the fund 2 years ago? b. With only $140,000 in the fund and 10 years remaining until your first child starts collego, what annual rate of return would 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 2 years, you fool the college fund has invested too much in stocks, and you want a low-risk lund in order to ensure you have the necessary $420,000 in 40 years. You are willing to make end of the month deposits to the fund as well you find you can get a lund that promises to pay a guaranteed annual return of 6 percent which 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 into this new fund? d. After seeing how large the monthly deposit would be (in part of this problem), you decide to invest the $140,000 today and S500 at the end of each month for the next 10 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