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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?

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Answer:

Annual deposit= $23,339.36

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

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