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 $35,000 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 5%. He currently has $205,000 saved, and he expects to earn 10% 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 your intermediate calculations. Round your answer to the nearest cent.

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Answer 1

He needs the same purchasing power for $35000 as today in 10 years, which means we need to adjust it for inflation -

Amount required each year after adjusting inflation = $35000 x (1 + inflation rate)ⁿ = $35000 x (1 + 0.05)¹⁰ = $57,011.31

Now, he needs the above amount for additional 24 years after the intial first payment and at beginning of each year (25 payments in total). We compute the present value of the same 10 years from now -

Present value of retirement income = $57,011.31 x (1+ PVIFA (10%, 24) = $57,011.31 x (1 + 8.98474401943) = $569,243.34

Also, he currently has $205,000 in his account which will earn 10% compounded annually. Future value (FV) of the same in 10 years -

FV of savings = $205,000 x (1 + r)ⁿ = $205,000 x (1 + 0.10)¹⁰ = $531,717.20

So, Amount needed in 10 years = Total retirement income desired - Savings = $569,243.34 - $531,717.20 = $37,526.14

This is the additional amount needed in 10 years. This is the future value of the annual deposits that he needs to make for 10 years. So, we have -

Annual deposits = $37,526.14 / PVIFA (10%, 10) = $37,526.14 / = $6,107.21