0
$\begingroup$

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?

$\endgroup$
0
$\begingroup$

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.

$\endgroup$
  • 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.