You inherit $500,000 from your parents and want to use the money to supplement your retirement. You receive the money on your 65th birthday, the day you retire. You want to withdraw equal amounts at the end of each of the next 25 years. What constant amount can you withdraw each year and have nothing remaining at the end of 25 years if you are earning 6% interest per year? a. $20,000 b. $28,489 c. $33,574 d. $39,113

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Advanced Placement (AP)

27 October, 04:56

You inherit $500,000 from your parents and want to use the money to supplement your retirement. You receive the money on your 65th birthday, the day you retire. You want to withdraw equal amounts at the end of each of the next 25 years. What constant amount can you withdraw each year and have nothing remaining at the end of 25 years if you are earning 6% interest per year? a. $20,000 b. $28,489 c. $33,574 d. $39,113

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Fisher · Answer 1

Since nothing remains after 25 years, future value is 0

Present value is $500000

As he withdraws equal amounts yearly, we use the formulae for present value of annuity. We can treat 25 years as annuity.

P = PMT x ((1 - (1 / (1 + r) ^ n)) / r)

Where:

P = the present value of an annuity stream

PMT = the dollar amount of each annuity payment

r = the interest rate (also known as the discount rate)

n = the number of periods in which payments will be made

Present value of annuity (6%, 25 yrs) = P (1 - 1 / (1+0.06) ^25 / 0.06)

500000 = P ((1-1/4.291) / 0.06)

P is the periodic payment annually

Equating this with the total present value

500000 = P x (12.782)

P = 500000/12.782

P=39117

Answer should be d) $39113