I think you are on the wrong track.
This is not an annuity problem, it is a cash flow/compound interest problem. The annuity formula only helps you when you have equal payments spread out over time.
Starting balance = 42,180.53
Annual contributions = 5,000.00 (contributed at end of year)
Expected return of 12%.
The logic is this: You start with 42,180.53 at "time 0" and the assumption is that this will earn 12% for the first year. So, at end of year 1, you have 42,180.52 * 1.12 = 47242.19. Add 5,000.
Now, balance at begining of Time 1 = 52,242.19. This earns 12%. Balance at end of time 1 is 58,511.25. Add the 5,000.
Balance at begining of Time 2 is 63,411.26, at 12 %, end of year balance is 71,132.61..add the 5,000. New balance is 76,132.61 at end of time 2/beginning of time 3.
Keep iterating the numbers. Answer is ....
Found in the movie Spinal Tap on Nigel's amplifier.
" This one goes to ______"