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:

$CRF={\frac {i(1+i)^{n}}{(1+i)^{n}-1}}$

where $n$ 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 $n=1$ , the $CRF$ reduces to $1+i$ . Also, as $n\to \infty$ , the $CRF\to i$ .

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

Calculator by Jenkins at University of California Archived July 8, 2006, at the Wayback Machine
"Capital Recovery Factor". www.homerenergy.com. Retrieved 2019-03-18.

External links

Wolfram|Alpha Capital Recovery Factor Calculator

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[1] Calculator by Jenkins at University of California Archived July 8, 2006, at the Wayback Machine

[:0-2] "Capital Recovery Factor". www.homerenergy.com. Retrieved 2019-03-18.