Question

Frank and Miranda would like to plan for their son’s college education. They would like their son, who was born today, to attend a private university for 4 years beginning at age 18. Tuition is currently $70,000 per year and has increased at an annual rate of 6%, while inflation has only increased at 3% per year. They can earn an after-tax rate of return of 8%. How much must they save at the end of each year if they would like to make the last payment at the beginning of their son’s first year of college?

Answer 1

Annual deposit= $23,339.36

Step-by-step explanation:

Giving the following information:

Tuition= $70,000

Number of years= 18

Interest rate= 8%

Growth rate= 6%

First, we need to calculate the total future value required:

FV= PV*(1+i)^n

Year 1= 70,000*1.06^18= 199,803.74

Year 2= 199,803.74*1.06= 211,791.97

Year 3= 211,791.97*1.06= 224,499.48

Year 4= 224,499.48*1.06= 237,969.45

Total FV= $874,064.64

Now, to calculate the annual deposit, 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= (874,064.64*0.08) / [(1.08^18) - 1]

A= $23,339.36