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.[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 {\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} .
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]
Wolfram|Alpha Capital Recovery Factor Calculator
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