ClueLuma

Level annual loan payment calculator

The capital-recovery factor converts principal to equal end-of-year payments at a positive interest rate.

Apay=P×i×(1+i)n(1+i)n−1A_{\text{pay}} = \frac{P \times i \times \left(1 + i\right)^{n}}{\left(1 + i\right)^{n} - 1}

Calculator

Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.

$
fraction
year
$/yr

Worked example

Given

  • PP = 250,000 $
  • ii = 0.06 fraction
  • nn = 10 year
Apay=250,000×0.06×(1+0.06)10(1+0.06)10−1≈33,967A_{\text{pay}} = \frac{250{,}000 \times 0.06 \times \left(1 + 0.06\right)^{10}}{\left(1 + 0.06\right)^{10} - 1} \approx 33{,}967

Symbols and units

SymbolMeaningUnit
ApayA_{\text{pay}}annual end-of-year payment$/yr
PPloan principal$
iiannual interest fractionfraction
nnnumber of annual paymentsyear

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Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.