A father wants to save for his 8-year-old son\'s college expenses. The son will

Question

A father wants to save for his 8-year-old son's college expenses. The son will enter college 10 years from now. An annual amount of $40,000 in constant dollars will be required in order to support the son's college expenses for 4 years. Assume that these college payments will be made at the beginning of the school year. The future general inflation rate is estimated to be 6% per year, and the market interest rate on the savings account will average 8% compounded annually. (a)What is the amount of the son's freshman-year expense in terms of actual dollars? (b)What is the equivalent single-sum amount at the present time for these college expenses? (c)What is the equal amount, in actual dollars, the father must save each year until his son goes to college? Given: i = 8% per year, f = 6% per year (a) Freshman-year expense in actual dollars: $40,000(F/P, 6%, 10) = $71,634 (b)Equivalent single-sum amount at n = 0 i' =(i-f)/(1+f) = (0.08-0.06)/(1+0.06) =0.01887 P = [$40,000(P/A, 1.887%, 3) + $40,000] (P/F, 1.887%, 10) = $129,077 (c)Required annual deposit in actual dollars: A = $129,077(A/P, 8%, 10) = $19,236

Explanation / Answer

First of all, we have to adjust the interest for the inflation. The relation between real and nominal interest rates and the expected inflation rate is given by the Fisher equation.:

Real rate =(nominal rate-inflation)/(1+inflation)

=(0.08-0.06)/(1+0.06)

=0.01887

So, now this is the interest rate that we would use to calculate the present value of amount.

Since the payment is to be made at the beginning of the year, the equivalent numbers of years will be = 4-1 = 3

So first we calculate the present value of annuity for 3 years.=[40,000(P/A,1.877%,3)]

Now since, there is still 10 years for his son to reach the college, we again discount the amount for 10 years = [40,000(P/A,1.877%,3)]*(P/F, 1.887%,10)

=129077

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