(Nonannual compounding using a calculator) Should we have bet the kids' college fund at the dog track? Let's look at one specific case of a college professor (let's call him Prof. ME) with two young children. Three years ago, Prof. ME invested $170,000 hoping to have $420,000 available 14 years later when his first child started college. However, the account's balance is now only $150,000. Let's figure out what is needed to get Prof. ME's college savings plan back on track.

a. If Prof. ME invested $170,000 into a fund 3 years ago and hoped to have $420,000 available 14 years later when his first child started college, what was the original APR needed to reach his goal? ___% (Round to two decimal places.)

b. Now with only $150,000 in the fund and 11 years remaining until his first child starts college, what APR would the fund have to earn to reach Prof. ME's $420,000 goal if he adds nothing to the account? __% (Round to two decimal places.)

c. If Prof. ME decides to transfer the $150,000 to a new fund that promises to pay a guaranteed APR of 5.5 percent compounded monthly and makes the necessary end-of-the-month deposits, how large of a monthly deposit must he make into this new fund to meet his $420,000 goal in 11 years? $___ (Round to the nearest cent.)

d. Now Prof. ME decides to invest the $150,000 today and $500 at the end of each month for the next 11 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 for Prof. ME to reach his $420,000 goal? __% (Round to two decimal places.)