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Today is your 24th birthday, and you decide to save $12,000 each year (with the first deposit one year from now) in an account paying 7% p.a., compounded annually. You will make your last deposit when you retire at age 65. You have a life expectancy of 90 years. How much money would you be able to withdraw per year after your retirement, if the first withdrawal occurs on your 66th birthday? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)

Question

Today is your 24th birthday, and you decide to save $12,000 each year (with the first deposit one year from now) in an account paying 7% p.a., compounded annually. You will make your last deposit when you retire at age 65. You have a life expectancy of 90 years. How much money would you be able to withdraw per year after your retirement, if the first withdrawal occurs on your 66th birthday? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)

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Solution

To solve this problem, we need to first calculate the total amount of money saved by the time of retirement, and then calculate the annual withdrawal amount.

Step 1: Calculate the total savings at retirement

The savings account grows annually at a rate of 7%, and you make a deposit of $12,000 each year for 41 years (from age 24 to 65). This is a future value of a series problem, which can be solved using the formula:

FV = P * [(1 + r)^n - 1] / r

where: FV = future value of the series P = annual deposit = $12,000 r = annual interest rate = 7% = 0.07 n = number of years = 65 - 24 = 41

Substituting the values into the formula, we get:

FV = $12,000 * [(1 + 0.07)^41 - 1] / 0.07

Step 2: Calculate the annual withdrawal amount

The total savings at retirement will be used to fund the annual withdrawals for 25 years (from age 66 to 90). This is a present value of a series problem, which can be solved using the formula:

PMT = PV * r / [1 - (1 + r)^-n]

where: PMT = annual withdrawal amount PV = present value = total savings at retirement r = annual interest rate = 7% = 0.07 n = number of years = 90 - 65 = 25

Substituting the values into the formula, we get:

PMT = FV * 0.07 / [1 - (1 + 0.07)^-25]

Finally, round the answer to 2 decimal places.

This problem has been solved

Similar Questions

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