Question

A father wants to save for his eight?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 to support the son�s college expenses for four years. Assume that these college payments will be made at the beginning of each 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?

Answer 1

Answer:

Instructions are listed below

Explanation:

Giving the following information:

The son will enter college 10 years from now. An annual amount of $40,000 in constant dollars will be required to support the son's college expenses for four years.

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) We need to find the present value for each 40,000-year expense.

Formula= FV/(1+i)^n

1: PV= 40,000/(1.06)^10= 22,335.80

2: PV= 40,000/(1.06)^11= 21,071.50

3: PV= 19,878.77

4: PV= 18,753.56

B) Total final value= 160,000

PV= 160,000/1.06^10= $89,343.16

C) We need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (160,000*0.06)/[(1.06^10)-1]= $12,138