Question

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $55,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 4%. He currently has $80,000 saved, and he expects to earn 7% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

1. First Annual Retirement Payment = Current Purchase Price * (1 + r)^10

First Annual Retirement Payment = 55000 * (1 + 0.04)^10

First Annual Retirement Payment = $81413.44

2. Future Value of Total Amount of 25 Payments at Year 85 age = First Annual Payment * FVAF(0.04,25)

Future Value of Total Amount of 25 Payments at Year 85 age = $81413.44 * 41.65

Future Value of Total Amount of 25 Payments at Year 85 age = $3390536.48

3. Present Value of Future Value at Savings Interest rate = $3390536.48 / (1 + r)^35

Present Value of Future Value at Savings Interest rate = $3390536.48 / (1 + 0.07)^35

Present Value of Future Value at year 50 age at Savings Interest rate = $317567.61

4. Amount Needed in present Value = 317567.61 - 80000 = $237567.61

5. Annual Deposit Required = Amount Needed / PVAF ( 0.07,10)

Annual Deposit Required = 237567.61 / 7.0236

Annual Deposit Required = $33824.28