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In: Finance

You put aside $100,000 in year t = 0, and let it grow at 7.1% interest...

You put aside $100,000 in year t = 0, and let it grow at 7.1% interest for 3 years. Exactly one year after that you start to withdraw your money for 4 years in equal amounts until it is exhausted. How much can you withdraw per year? Answer to the nearest cent, xxx.xx and enter without a dollar sign.

Expert Solution

$100,000 grows at 7.1% per year for 3 years

Value after 3 years = 100,000 X (1+7.1%)^{3 =} $122,848

The investment is kept for another year

Value after 4 years = 122,848 X (1+7.1%) = $131,570 ---------------(1)

Let Y be the amount withdrawn each year

The present value of all the withdrawals at year 4 can be calculated using the PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = annual interest rate = 7.1%

number of periods = 4

payment amount = yearly withdrawal = 1 ----- here Y isn't given as the formula will give an error. The PV value can be multiplied with Y to get the desired result

future value = future value of investments = 0

when-due = when is the investment made each year = beginning = 1

The present value of all the withdrawals at year 4 = PV(7.1%, 4, 1, 0, 1)*Y

= 3.62Y -------------------(2)

Equation (1) = Equation (2)

implies, 131,570 = 3.62Y

Y = 36,350.12

You can withdraw 36,350.12 per year

jeff jeffy answered 2 years ago

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