Question

You would like your child, who was born today, to attend a private university for 4 years beginning at age 18. Tuition is currently $20,000 per year and has increased 5% annually. Your after-tax rate of return is 8%. How much must you save at the end of each year if you would like to make your last payment at the beginning of your child's first year of college?

Answer 1

Annual deposit= $5,539.52

Step-by-step explanation:

First, we need to calculate the total worth of the 4 years tuition 18 years from now:

FV= PV*(1+i)^n

Year 1= 20,000*1.05^18= 48,132.39

Year 2= 48,132.39*1.05= 50,539

Year 3= 50,539*1.05= 53,065.95

Year 4= 53,065.95*1.05= 55,719.25

Total FV= $207,456.59

Now, using the following formula we can determine the annual deposit:

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

A= annual deposit

Isolating A:

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

A= (207,456.59*0.08) / [(1.08^18) - 1]

A= $5,539.52