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(Nonannual compounding using a calculator​) Should we have bet the​ kids' college fund at the dog​...

(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. Two years​ ago, Prof. ME invested ​$ 180,000 hoping to have ​$ 420,000 available 11 years later when his first child started college. ​ However, the​ account's balance is now only ​$ 160,000. ​Let's figure out what is needed to get Prof.​ ME's college savings plan back on track.

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

  1. Now with only ​$ 160,000 in the fund and 9 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?

  1. 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 ​$420,000 in 9 ​years, and he is willing to make​ end-of-the-month deposits to the fund as well. He later finds a fund that promises to pay a guaranteed APR of 6 percent compounded monthly. Prof. ME decides to transfer the ​$ 160,000 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?

  1. 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 ​$160,000 today and ​$500 at the end of each month for the next 9 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?

  1. If Prof. ME invested ​$180,000 into a fund 2 years ago and hoped to have ​$ 420,000available 11 years later when his first child started​ college, what was the original APR needed to reach his​ goal?

% (Round to two decimal places)

  1. b. Now with only ​$160,000 in the fund and 9 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)

  1. c. If Prof. ME decides to transfer the ​$160,000 to a new fund that promises to pay a guaranteed APR of 6 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 9 ​years?

$ (Round to the nearest cent)

  1. d. Now Prof. ME decides to invest the ​$160,000 today and ​$500 at the end of each month for the next 9 years into a fund consisting of 50 percent stock and 50 percent​ bonds, and hope for the best. What APR would the fund have to earn for Prof. ME to reach his ​$ ​goal?

% (Round to two decimal places)

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