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.

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.

In the limit of zero interest rate, \lim_{i\rightarrow 0} CRF = 1/n (L'Hôpital's rule).