I don't get the point in the "stages" or why you need to test $2000. There isn't any point to that, unless you just want to see it. You also do not need to use Excel. It looks like you're using a financial calculator to do this. If that is what is required in class or the way you choose to do it, that is fine. (And Rolcam, there is absolutely no explanation in your answer of how you came up with any of that stuff.)
What you're messed up on to begin with is in deciding if this is an annuity or not. If you're going to "make payments annually" it's an annuity. An annuity involves some type of payment, either being put into something or taken out of something. When you have payments like that, NEVER use FV and PV together. They won't exist together like you tried to do first. (It only works for lump sums, e.g. you stick money into something and just let it sit and earn interest, but don't add more payments to it.)
This is a sinking fund - making payments to save up for something you need in the future. That's always an annuity.
So your second attempt is the basic idea. Except that I don't know how you got your answer. If you're using a calculator, it means you're entering it into the calculator incorrectly somehow. As a matter of fact, even if this were a lump sum instead of an annuity, you first answer isn't correct. So I'm not sure what you're doing wrong in the calculator.
You've got the N=8, I/YR=12, FV=30,000. That's all OK. Some ideas:
You didn't include P/YR (or whatever yours calls it). That is, you have 1 payment per year. It needs to know how often it's compounding.
With my calculator, whatever I stick into these keys will stay. If I do a new problem, anything I don't replace stays there. For instance, if I did one where I used PV and this problem doesn't use it, the PV from the prior problem stays there and gets calculated into the thing screwing it up. I have to "clear" anything I don't want (and the answer I want in case I used it) by entering zero.
For instance, I entered N=8, I/YR=12, PV=0 (to clear), PMT=0 (to clear, even tho that's the answer I want), FV=30,000, and P/YR=1. Then I hit the PMT key to get my answer. I don't know if your calculator has this issue.
I assume COMP is compute, but you aren't telling it what to compute that I can see. Something is just seems missing somewhere.
As for the 2177.75 Rolcam came up with, that's based on the assumption of an annuity due. That's when payments are made at the beginning of the period. Unless the problem says otherwise, it's generally assumed to be at the end of the period. Does the problem say anything about this? (Don't leave things out of problems when you present them to us.) If not, I'm assuming at the end of each year.
