Professor Vélez has withdrawn 40 monthly payments of $3,275 from her investment account. If the investment account yields 4% convertible monthly, how much did you have in your investment account one month before making the first withdrawal? (Since you started making withdrawals you have not made any deposits.)

To find out how much was in the investment account one month before making the first withdrawal, we need to work backwards.

Let's assume that the amount in the account one month after the first withdrawal is A.

Since the account yields 4% convertible monthly, the amount after one month will be given by:

A = (1 + 0.04) * (initial amount - first withdrawal)

Now, we can find the initial amount by rearranging the equation:

initial amount = A / (1 + 0.04) + first withdrawal

Substituting the values given:

first withdrawal = $3,275
A = $3,275 (since one month has passed since the first withdrawal)

initial amount = $3,275 / (1 + 0.04) + $3,275

Simplifying:

initial amount = $3,275 / 1.04 + $3,275

Calculating:

initial amount = $3,150 + $3,275

Answer: The amount in the investment account one month before making the first withdrawal was $\$6,425.96