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Capital recovery factor

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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:

C R F = i ( 1 + i ) n ( 1 + i ) n − 1 {\displaystyle CRF={\frac {i(1+i)^{n}}{(1+i)^{n}-1}}}

where n {\displaystyle n} is the number of annuities received.

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 {\displaystyle n=1} , the C R F {\displaystyle CRF} reduces to 1 + i {\displaystyle 1+i} . Also, as n → ∞ {\displaystyle n\to \infty } , the C R F → i {\displaystyle 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.

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.

References

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

External links

Wolfram|Alpha Capital Recovery Factor Calculator

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