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Annual Worth Calculator

Enter a present value, interest rate, and number of years to find the equivalent annual worth.

Result

$7,451.47
0.149029
$74,514.74

How it is calculated

The tool spreads a present sum over n equal year-end payments with the capital recovery factor: A/P = i(1+i)n ÷ ((1+i)n − 1) and AW = PV × A/P. PV is the present value in dollars, i is the annual interest rate as a decimal (the field takes percent, so 8 becomes 0.08) and n is the number of years.

It also shows the factor to six decimals and the sum of all payments, AW × n, so you can see how much interest is paid over the period. The rate must be above 0 (a 0% rate gives no result, although in theory it would be PV ÷ n) and n must be at least 1. Payments are assumed to occur at the end of each year, with interest compounded annually.

Worked example

An equipment purchase of $50,000 is financed at 8% over 10 years. Growth factor (1.08)10 = 2.158925. Capital recovery factor = 0.08 × 2.158925 ÷ (2.158925 − 1) = 0.149029. Annual worth = 50,000 × 0.149029 = $7,451.47 per year. Over 10 years the payments add up to $74,514.74, so about $24,514.74 of that is interest.

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Common mistakes

  • Typing the rate as 0.08 instead of 8. The field is in percent, so 0.08 means 0.08% and the annual worth would be almost PV ÷ n.
  • Entering monthly payments' rate with years, or the other way round. Rate and period must both be annual here.
  • Expecting payments at the start of each year. The factor assumes end-of-year payments; an annuity due is slightly smaller.
  • Entering a 0% rate to split a sum evenly. The tool needs a rate above 0, so divide PV by n yourself in that case.
  • Comparing alternatives with different interest rates or risk. Annual worth is only fair when the same rate is applied to every option.

About this calculator

In engineering economics, annual worth (AW) converts a lump-sum present value into an equivalent uniform series of payments spread over n years — the same amount of money each year that, discounted back at the given interest rate, equals the original present value. The conversion uses the capital recovery factor, A/P = i(1+i)^n / [(1+i)^n − 1], the standard formula for turning a present sum into a level annuity.

Annual worth analysis is especially useful for comparing investments or equipment with different service lives, since converting each alternative to an “equivalent cost or benefit per year” puts them on the same footing without needing a common analysis period the way net present value comparisons sometimes require. It is a staple technique in capital budgeting, project selection and cost-benefit analysis taught alongside present worth and internal rate of return.

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Comments (1)

  • Editorial team

    Annual worth makes projects with different lives comparable, but only when they cover the same service and costs repeat. For a present value of 10000 at 7% over 10 years the tool gives 1,423.78 a year, a factor of 0.142378 and 14,237.75 paid in total. It handles one upfront sum, with no salvage value or varying cash flows. Which two alternatives are you comparing?

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