Question - Nonannual compounding using a calculator

Should we have bet the kids' college fund at the dog track? In the downturn of 2008-2009 investors suffered substantial declines on tax-sheltered college savings plans (called 529 plans) around the country. Let's look at one specific case of a college professor (let's call him Prof. ME) with two young children. Two years ago Prof. ME invested $160,000 hoping to have $420,000 available 12 years later when the first child started college. However, the account's balance is now only $140,000. Let's figure out what is needed to get Prof. ME's college savings plan back on track.

a. What was the original annual rate of return needed to reach Prof. ME's goal when he started the fund 2 years ago?

b. Now with only $140,000 in the fund and 10 years remaining until his first child starts college, what annual rate of return would the fund have to earn to reach Prof. ME's $420,000 goal if he adds nothing to the account?

c. Shocked by his experience of the past 2 years, Prof. ME feels the college mutual fund has invested too much in stocks. He wants a low-risk fund in order to ensure he has the necessary $420,000 in 10 years, and he is willing to make end-of-the-month deposits to the fund as well. He later finds a fund that promises to pay a guaranteed return of 6 percent compounded monthly. Prof. ME decides to transfer the $140,000 to this new fund and make the necessary monthly deposits. How large of a monthly deposit must Prof. ME make into this new fund to meet his $420,000 goal?

d. Now Prof. ME gets sticker shock from the necessary monthly deposit he has to make into the guaranteed fund in the preceding question. He decides to invest the $140,000 today and $500 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 annual rate of return would the fund have to earn in order to reach Prof. ME's $420,000 goal?