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A college professor ( Prof . M ) has two young children. Two years ago, Prof. M invested $ 1 8 0 comma 0 0
A college professorProf M has two young children. Two years ago, Prof. M invested $ comma in a fund hoping to have $ comma available years later when his first child started college. However, the account's balance is now only $ comma
a What was the original annual rate of return needed to reach Prof. Ms goal when he invested in the fund years ago?
b Now with only $ comma in the fund and years remaining until his first child starts college, what APR would the fund have to earn to reach Prof. Ms goal of$ comma if he adds nothing to the account?
c Shocked by his experience of the past years Prof. M now wants to invest in a new fund and is willing to make endofmonth deposits into the fund so that he has the necessary $ comma in years. The new fund promises to pay a guaranteed APR of percent compounded monthly. Prof. M decides to transfer the $ comma to this new fund and make the necessary monthly deposits. How large of a monthly deposit must Prof. M make into this new fund to meet his $ comma goal
d Now Prof. M gets sticker shock from the necessary monthly deposit he has to make into the new fund in the preceding question. He decides to invest the $ comma today and $ at the end of each month for the next years into this fund since that is all he can afford. What APR would the fund have to earn for Prof. M to reach his $ comma goal
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