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?



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.

  • 1
    $\begingroup$ 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! $\endgroup$ – Duci Apr 27 at 8:49

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