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Capital Recovery Factor Calculator

Enter the interest rate, number of periods, and present sum to find the periodic payment.

How it is calculated

The capital recovery factor says how much level payment per period repays one unit of present money, interest included. With i = rate ÷ 100 as the interest rate per period and n as the number of periods, CRF = i × (1+i)^n ÷ ((1+i)^n − 1). The level payment is payment = present sum × CRF, and the total paid is payment × n. The rate is entered as a percentage per period, so it must match the period: use a monthly rate with a number of months, or an annual rate with a number of years. The rate must be above zero, because at 0% the formula breaks down and the tool returns no result, and n must be at least 1. The formula assumes payments at the end of each period and a constant rate. Amounts are shown in dollars with two decimals and the factor with six.

Worked example

Recover $50,000 over 10 years at 8% per year. First the growth factor: 1.08^10 = 2.158925. CRF = 0.08 × 2.158925 ÷ (2.158925 − 1) = 0.172714 ÷ 1.158925 = 0.149029. Payment: 50,000 × 0.149029 = $7,451.47 per year. Total paid: 7,451.47 × 10 = $74,514.74, which means $24,514.74 of the total is interest. The CRF of 0.149029 also tells you that each dollar borrowed costs about 14.9 cents a year over this term.

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Common mistakes

  • Mixing the rate and period units. An annual 8% with 120 months gives a wrong, far too low payment; use 8 with 10 years, or about 0.6667 with 120 months.
  • Entering the rate as a fraction (0.08) instead of a percentage (8). The tool would treat it as 0.08% a period.
  • Entering 0 for an interest-free loan. The tool returns no result at a zero rate; divide the present sum by n yourself in that case.
  • Forgetting the payments are assumed at the end of each period. If payments start immediately, the true payment is slightly smaller.
  • Comparing totals of options with different n without looking at the time value of money. A higher total over a longer span is not necessarily worse.

About this calculator

The capital recovery factor (CRF) converts a present lump sum into a series of equal periodic payments that fully repay that sum, including interest, over a set number of periods. It's calculated as CRF = i(1+i)^n / ((1+i)^n − 1), where i is the interest rate per period and n is the number of periods — the same formula that underlies standard loan amortization.

Multiplying the present sum by the CRF gives the level payment needed each period. This calculator computes both the factor and that payment from your interest rate, number of periods, and present sum. It's a core tool in engineering economics and capital budgeting, used to compare equipment purchases, evaluate lease-versus-buy decisions, or figure out what a loan or investment payback actually costs per period.

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Comments (1)

  • Editorial team

    The rate and the count must use the same period, and the payment lands at the end of each one. For 10,000 at 5% over 10 years the tool gives 1,295.05 a year. Monthly payments need a monthly rate and 120 periods: 5% divided by 12 over 120 periods gives 106.07 a month and 12,727.86 in total, a different picture from yearly. Are you using it for equipment replacement or a loan?

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