A capital recovery factor is the ratio of a constant

annuity In investment, an annuity is a series of payments made at equal intervals.Kellison, Stephen G. (1970). ''The Theory of Interest''. Homewood, Illinois: Richard D. Irwin, Inc. p. 45 Examples of annuities are regular deposits to a savings account, ...

to the

present value In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...

of receiving that annuity for a given length of time. Using an

interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...

''i'', the capital recovery factor is:

CRF = \frac

where

n

is the number of annuities received.Calculator by Jenkins at University of California
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.{{Cite web, url=https://www.homerenergy.com/products/pro/docs/3.11/capital_recovery_factor.html, title=Capital Recovery Factor, website=www.homerenergy.com, access-date=2019-03-18 Another reading that can be obtained is that the

net present value The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount ...

of 10 annual payments of $163 at 10% discount rate is $1,000.

References

External links

Wolfram, Alpha Capital Recovery Factor Calculator
Financial ratios Annuities