Capital recovery factor explained

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 = (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 inf ty , 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.

References

1. http://faculty.engineering.ucdavis.edu/jenkins/CBC/Calculator/CalculatorBackground.pdf Calculator by Jenkins at University of California
2. Web site: Capital Recovery Factor. www.homerenergy.com. 2019-03-18.

External links

Wolfram|Alpha Capital Recovery Factor Calculator