engineering economy question

[tonyd]

To withdraw the following $1,000 payment series, determine the minimum deposit (P) you should make now if your deposits earn an interest rate of 10%, compounded annually. Note that you are making another deposit at the end of year 7 in the amount of $500. With the minimum deposit P, your balance at the end of year 10 should be zero.

 

[tonyd]

The diagram is a bit weird with deposits shown as negatives and withdrawals as positives.

Do you know the formulas for present and future values of an amount and of a deferred annuity? You can attack this problem either in terms of present or future value, but it is probably more intuitive to use the formulas for future value. Alternatively, this kind of problem is readily solved through a spread sheet.

I know all of the formulas. I tried doing:

1000(P/A,10%,6) - 500 + 1000(P/A,10%,3)(P/F,10%,7) = 5131.58

But this is incorrect, I'm missing something somewhere.

 

[tonyd]

I found the correct answer using the NPV function on Excel. But I'm still interested in learning how to do it without Excel