Carolyn has just retired, and has 400000 dollars in her retirement account. The account will earn interest at an annual rate of 6 percent, compounded monthly. At the end of each month, Carolyn will withdraw a fixed amount to cover her living expenses. Carolyn wants her savings to last exactly 20 years. How much money can she withdraw each month? (Give your answer in dollars, correct to the nearest cent.) monthly withdrawal: Incorrect: Your answer is incorrect. What is the maximum amount that Carolyn can withdraw each month if she wants her savings to last indefinitely? monthly withdrawal: Incorrect: Your answer is incorrect.

You want to know the amount Carolyn can withdraw from a $400,000 account earning 6% compounded monthly if (a) it is to last 20 years, and (b) it is to last indefinitely.

(a) Annuity

The withdrawal amount from an ordinary annuity is given by the formula ...

A = P(r/12)/(1 -(1 +r/12)^-n)

where P is the amount invested at annual rate r, and n monthly withdrawals are made.

For the given conditions, the amount Carolyn can withdraw is ...

A = 400000(0.06/12)/(1 -(1 +0.06/12)^-240) ≈ 2865.72

Carolyn can withdraw $2865.72 at the end of each month if she wants it to last 20 years.

(b) Interest

If Carolyn wants her fund to last indefinitely, she can only withdraw the interest earned each month:

I = Prt . . . . . . where P is invested at annual rate r for t years

One month is 1/12 year, so the interest earned is ...

I = 400000(0.06)(1/12) = 2000.00

Carolyn can withdraw $2000 at the end of each month if she wants her account to last indefinitely.