You have $39,000 in an account earning an interest rate of 4%. What are the equal...

You have $39,000 in an account earning an interest rate of 4%. What are the equal beginning-of-month withdrawals you can make from this account such that it is completely depleted with the last withdrawal at the beginning of the last month in 22 years? Round to the nearest cent. [Hint: The amount in the account today is the PV of an annuity due where the withdrawals are the annuity cash flows. There will be a total of 22 x 12 withdrawals.]

Expert Solution

Monthly rate = 4% / 12 = 0.333333%

Number of periods = 22 * 12 = 264

Presnet value = (1 + r) * Annuity * [1 - 1 / (1 + r)^n] / r

39,000 = (1 + 0.00333333) * Annuity * [1 - 1 / (1 + 0.00333333)^264] / 0.00333333

39,000 = 1.00333333 * Annuity * [1 - 0.415391] / 0.00333333

39,000 = 1.00333333 * Annuity * 175.382959

39,000 = Annuity * 175.967569

Annuity = $221.63

Monthly withdrawals will be $221.63

jeff jeffy answered 2 years ago

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You have $39,000 in an account earning an interest rate of 4%. What are the equal...

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