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There is a formula for this. It is FV = (i * (n+1)/2 * P) + P where P, n, and i have the definitions given in your post.
For example, P=50,000, n = 10, and i = .08, then FV = (.08 *(10+1) / 2 * 50000) + 50000 = (.88 / 2 * 50000) + 50000 = 22000 + 50000 = 72000. This can be proven by stepping through the calculations for each period. Interest at end of first period = 4000, therefore payment = 50000/10 + 4000 = 9000, etc. Add it all up at the end and you will prove the answer.
This assumes that the payments are not reinvested - that would complicate things significantly.
If you need further information or assistance, please let me know.
I think there must be a mistake in there somewhere. If the one plan has a single payment at the end, then interest will continue on the full amount of principal for the entire n periods. The other plan reduces principal each of the n periods and, therefore, cannot possibly have the same FV unless there are other factors that are being considered.
Please make sure that the problem is stated correctly and if there are any other variables or circumstances that are to be considered.
Glad I could help some.
Let me know if you need anything else.