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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?

Brydon Gibson
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1 Answers1

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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.

timodwhit
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