​(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 ​$440,000 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. What was the original annual rate of return needed to reach Prof.​ ME's goal when he started the fund 3 years​ ago? 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 ​$440,000 goal if he adds nothing to the​ account? c. Shocked by his experience of the past 3 ​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 ​$440,000 in 11 ​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 5 percent compounded monthly. Prof. ME decides to transfer the ​$150,000 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 ​$440,000 ​goal?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
​(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
​$440,000
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. What was the original annual rate of return needed to reach Prof.​ ME's goal when he started the fund
3
years​ ago?
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
​$440,000
goal if he adds nothing to the​ account?
c. Shocked by his experience of the past
3
​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
​$440,000
in
11
​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
5
percent compounded monthly. Prof. ME decides to transfer the
​$150,000
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
​$440,000
​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
​$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
​$440,000
​goal?
 
 
 
a. If Prof. ME invested
​$170,000
into a fund
3
years ago and hoped to have
​$440,000
available
14
years later when his first child started​ college, what was the original APR needed to reach his​ goal?
 
nothing​%
​(Round to two decimal​ places.)
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