Ok if I have the formula for future value of an annuity:
FVAn = PMT sum (1+i)^(n-t)
I can't do greek characters so forgive the sum sign; t=1 is below the sigma and n above.
How do I solve for n?
FVAn = 42,180.5
PMT = 5000
i = 12% or .12
n is unknown
I want 42,180.53 and the account is 12% annually and I can make payments 5,000 a year, so how many years will it take (n)??
I'm trying to figure this as part of the larger problem which reads:
John has $42,180.53 in a brokerage account, and he plans to contribute an additional $5,000 to the account at the end of every year. The brokerage account account has an expected annual return of 12 percent. If John's goal is to accumulate $250,000, how many years will it take?
I figure if I equate the 42,180.53 in terms of years (compounded of the payments 5,000). Then I can do a reverse ammortization from 250k and 5k payments, find the number of years and then subtract the equivalent years that the 42,180.53 equals.
any ideas, I know I can use a financial calculator but I want to understand the math behind it....
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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 ....
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