Is there an easy way to determine the present worth (PV) of an annuity when the annuity is increasing by a fixed value, not a percentage? Ie. A contract pays you 10 000 the first year, 13 000 the second, 16 000 the third and so on, increasing by 3000 each year.
I know that for increasing by a specific percentage the formula is: $\frac{P}{i-g}[1-(\frac{1+g}{1+r})^n]$
Does it just require finding g in terms of n, such that the percentage changes, but the value stays the same? That seems more complicated than necessary, or does that result in a derivation that leads to a new formula?
If we break this down into simpler terms we get:
Year 1: 10000
Year 2: 10000 + 10000 + 3000
Year 3: 10000 + 10000 + 1000 + 3000 + 3000
Year N: 10000n + 3000(n-1) where n is the year.
Hope that helps.