How much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal

Question Completion:

Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires - that is, until he is 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $40,000 has today. He wants all his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5% per year from today forward. He currently has $100,000 saved up; and he expects to earn a return on his savings of 8% per year with annual compounding.

He must save $57,326.75 yearly for 10 years to meet his retirement goal.

Explanation:

a) Data and Calculations:

The future value of the first retirement payment of $40,000 = $86,360 ($40,000 * 2.159)

Future value factor = 2.159 at 8% for 10 years

Amount to be paid over 24 years = $960,000 ($40,000 * 24)

Total amount to be paid in 25 years of retirement = $1,046,360 ($960,000 +$86,360)

Future value of initial savings of $100,000 = $215,892.50

Amount expected to be saved in ten years = $830,467.50 ($1,046,360 - $215,892.50)

N (# of periods)  10

I/Y (Interest per year)  8

PV (Present Value)  0

FV (Future Value)  830467.50

Results

PMT = $57,326.75

Sum of all periodic payments$573,267.47

Total Interest$257,200.03