My example is saving for college:
- assume a start of 0 balance
- deposits of 200 made monthly, every year they increase by (g) 2% to account for salary increases, first deposit made at the end of the first month
- Interest Rate (r) is constant at 8% (effective rate)
- Goes for (n=15) years
What is the future value?
Even though I can convert the yearly rate into a compounded monthly rate to match the yearly rate, I can't use the "future value of a growing annuity" formula, that assumes timing of growth and payment are the same.
It is acceptable to make it a two or three steps (like use equation 1 to solve for a new value for payment to plug that into equation 2), I am just trying to avoid making calculations for each and every year as I'm doing now.
n(1) = 2486
n(2) = 5222.23
I found my own answer as well below that combines well known formulas to get to the same answer (and I presume, with substitution, would be equivalent to the accepted answer)