# Trying to re-write the formula for the present value of an annuity to solve for annuity value

I have the formula: $$PV = C * {{(1-(1+r)^{-n})} \over r}$$

This is the formula for the Present Value (PV) of an Annuity (C) with interest (r) (for example 5% interest is 0.05) over (n) periods.

I would like to rewrite the formula so that I can solve for C. For the life of me I cannot get it right for some reason. I know I could just google the formula, but I want to be able to re-write the formula on my own. Could someone be so kind to show me the steps on how to re-write this?

Hint:

Multiply by $$r$$ on both sides and then divide by $$(1 - (1+r)^{-n})$$ on both sides.

Alternate Hint:

Perhaps this might be easier to look at. You could look at this equation as having the form

$$a = xb$$

where $$a = PV, b = (1-(1+r)^{-n})/r, x = C$$. Solving for $$x$$ (equivalent to solving for $$C$$ since $$x=C$$) just amounts to dividing both sides by $$b$$. Then you would have $$x =a/b$$ and could substitute in the appropriate values.

• Thanks, it indeed helps to think of it in terms of a = xb. For me its not intuitive, yet, but with this I think I'll get there. Thanks again! – Duci Apr 27 at 8:49