Finance:Capital recovery factor
A capital recovery factor is the ratio of a constant annuity to the present value of receiving that annuity for a given length of time. Using an interest rate i, the capital recovery factor is: [math]\displaystyle{ CRF = \frac {i(1+i)^n}{(1+i)^n-1} }[/math]
where [math]\displaystyle{ n }[/math] is the number of annuities received.[1]
This is related to the annuity formula, which gives the present value in terms of the annuity, the interest rate, and the number of annuities.
If [math]\displaystyle{ n = 1 }[/math], the [math]\displaystyle{ CRF }[/math] reduces to [math]\displaystyle{ 1+i }[/math]. Also, as [math]\displaystyle{ n \to \infty }[/math], the [math]\displaystyle{ CRF \to i }[/math].
Example
With an interest rate of i = 10%, and n = 10 years, the CRF = 0.163. This means that a loan of $1,000 at 10% interest will be paid back with 10 annual payments of $163.[2]
Another reading that can be obtained is that the net present value of 10 annual payments of $163 at 10% discount rate is $1,000.[2]
References
External links
Wolfram|Alpha Capital Recovery Factor Calculator
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