Find the amount of money needed to be invested

Attached is a file with the question and all of my workproblem 137.pdf (94.2 KB)

Did you draw a time line? (Or maybe even more that one, to help you evaluate the pieces).

Your calculation for the withdrawals: You have an expression that includes a (1.08)^(-4) piece. Think first about just that expression, before you apply the 1.08^(-17) or 1.08^(-18) to it. It that the PV of the withdrawals at the moment of the first withdrawal, or one year after the first withdrawal, or some other term?

Given when that PV is evaluated, what do you have to multiply it by to get it to be the PV at the moment of the first deposit?

@gandalf Okay so I think i get what you mean I have four payments and the last payment is on the 21st year so 21-4=17. Is that correct? or am I missing something else?

i need verification

The first payment is at time 18. Either discount an annuity due eighteen years or an annuity immediate seventeen years.