Question

Deryl wishes to save money for his retirement and for the education of his son. His son will need $25,000 annually for four years beginning 15 years from now. Deryl wants to retire 31 years from now, and would like to have $100,000 annually for 25 years upon retirement (i.e., the first withdrawal starting on year 31). Given an interest rate of 9%, how much must Deryl invest annually, if he plans to begin making deposits in one year, and plans to make 30 deposits in all? (Use TVM function on calculator and show inputs (N, I/Y, PV, PMT, FV))

Answer 1

For sons education, His son will need $25,000 annually for four years beginning 15 years from now

We need to calculate PVA of 4 years beginning 15years from now.

N = 4

I/Y = 9

PMT = $25,000

FV = 0

Compute PV = 80993 (using Financial Calculator)

Now this becames Future Value and we need to compute PV for This amount

N = 15

I/Y = 9

PMT = 0

FV = -80993

Compute PV = 22,235.66 (using Financial Calculator)

For Retirement, Deryl wants to retire 31 years from now, and would like to have $100,000 annually for 25 years upon retirement

We need to calculate PVA of 25 years beginning 31 years from now.

N = 25

I/Y = 9

PMT = $100,000

FV = 0

Compute PV = 982257.96 (using Financial Calculator)

Now this becames Future Value and we need to compute PV for This amount

N = 31

I/Y = 9

PMT = 0

FV = -982257.96

Compute PV = 67,921.01 (using Financial Calculator)

Total Corpus Required = PV of sons education+ PV of Retirement corpus

Total Corpus Required = 22,235.66+67,921.01= 90156.67

This corpus is your PV. We need to find Annual Payment of he wishes to make 30 deposits

N = 30

I/Y = 9

PV = 90156.67(1.09) = 98270.77-- because he makes his first deposit in one year

FV = 0

Compute PMT =9565.32 (using Financial Calculator)

Therefore, He needs to make annual deposits of 9565.32 every year for next 30 years to save enough for retirement and his sons education.