Question

Let's say you deposited ​$150,000 in a 529 plan​ (a tax advantaged college savings​ plan) hoping to have ​$410,000 available 15 years later when your first child starts college. ​ However, you​ didn't invest very​ well, and 2 years later the account balance dropped to ​$130,000. ​ Let's look at what you need to do to get the college savings plan back on track. a.  What was the original annual rate of return needed to reach your goal when you started the fund 2 years​ ago? b. With only ​$130,000 in the fund and 13 years remaining until your first child starts​ college, what annual rate of return would the fund have to make to reach your ​$410,000 goal if you add nothing to the​ account? c.  Shocked by your experience of the past 2 ​years, you feel the college fund has invested too much in​ stocks, and you want a​ low-risk fund in order to ensure you have the necessary ​$410,000 in 13 years. You are willing to make​ end-of-the-month deposits to the fund as well. You find you can get a fund that promises to pay a guaranteed annual return of 4.5 percent which is compounded monthly. You decide to transfer the ​$130,000 to this new fund and make the necessary monthly deposits. How large of a monthly deposit must you make into this new​ fund? d.  After seeing how large the monthly deposit would be​ (in part c of this​ problem), you decide to invest the ​$130,000 today and ​$400 at the end of each month for the next 13 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 in order to reach your ​$410,000 ​goal? -Round to two decimal places

Answer 1

Part (a):

Amount invested (A)= $150,000

Value expected in 15 years= $410,000

Rate of return needed for reaching the above maturity value= [($410,000/$150,000)^(1/15)]-1

= (2.733333^0.066667)-1 = 6.93%

Part (b):

Amount available after 2 years= $130,000

Time left= 13 years.

Maturity value required= $410,000

Rate of return needed for reaching the above maturity value= [($410,000/$130,000)^(1/13)]-1

=( 3.153846^ 0.076923)-1= 9.24%

Part (c):

With reduced return of 4.5% per year compounded monthly and deposit of current amount of $130,000 in the scheme,

Monthly deposits needed to reach $410,000 in 13 years= $836.54 Calculated using PMT function of Excel as follows:

Part (d):

Together with the initial deposit of $130,000 and monthly deposits of $400 at the end of each month, APR needed to have the maturity value of $410,000 after 13 years = 11.13%

Calculated using RATE function of Excel as follows: