# Denis won a prize of \$25,000. He has decided to invest in an account paying 6.25% /a , compounded monthly. How much can he withdraw from the account each month over the next 3 years, starting in a month?

The maximum fixed amount that he can withdraw each month without getting into debt is \$787.29. Suppose he will withdraw the same amount each month. It may be a different amount; for example, he can withdraw `\$ 0 , ` or he can withdraw monthly interest to leave the same amount on the balance. I suppose the question is asking about the maximum amount that he can withdraw monthly without getting into debt so that, at the end, he will have zero at his account.

In this case, the amount on the account will decrease each month (except the first one), so we can use Present Value of an Ordinary Annuity formula:

`PV = ( P M T ) / i ( 1 - 1 / ( 1 + i )^n ) .`

Here month interest `i = 6.25 / 100 * 1 / 12 , ` "loan" amount is the amount after 1 month, in other words `PV = 25000 ( 1 + i ) , ` and the number of months is `3 * 12 - 1 = 35 . ` The monthly withdraw amount is `P M T ,` which we want to find.

This way,

`PMT = PV * ( i ( 1 + i )^n ) / ( ( 1 + i )^n - 1 ) = 25,000 * ( i ( 1 + i )^36 ) / ( ( 1 + i )^35 - 1 ) approx 787.29 (\$) .`