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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 $60,000 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 $185,000 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? Round your answer to the nearest cent.

Respuesta :

jepessoa

Answer:

$46,922.09

Explanation:

we must first determine the amount of money your father will receive in 10 years adjusted to inflation:

future value = $60,000 x (1 + 4%)¹⁰ = $88,814.66

I used an excel spreadsheet to calculate the other 24 payments. Since the retirement plan will continue to earn 10% per year, I calculated the present value of the distributions (when your father turns 60) = $1,227,639.71.

This means that your father's retirement account must have $1,227,639.71 by the time he turns 60 years old.

Your father currently has $185,000 which will gain interest and its future value = $185,000 x (1 + 10%)¹⁰ = $479,842.36

He will be $1,227,639.71 - $479,842.36 = $747,797.35 short.

In order to determine the annual contribution, we have the use the future value of an annuity formula:

  • future value = $747,797.35
  • FV annuity factor, 10%, 10 periods = 15.937

annual contribution = $747,797.35 / 15.937 = $46,922.09

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