ClueLuma

Base plus gradient annual equivalent calculator

Equivalent annual cost is calculated as A_base + G × [1/i − n/((1+i)^n−1)]. Use the stated system boundary and matching input units.

Aeq=Abase+G×[1i−n(1+i)n−1]A_{\text{eq}} = A_{\text{base}} + G \times \left[\frac{1}{i} - \frac{n}{\left(1 + i\right)^{n} - 1}\right]

Calculator

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

$/year
$/year
—
year
$/year

Worked example

Given

  • AbaseA_{\text{base}} = 5,000 $/year
  • GG = 500 $/year
  • ii = 0.08 —
  • nn = 10 year
Aeq=5000+500×[10.08−10(1+0.08)10−1]≈6,936A_{\text{eq}} = 5000 + 500 \times \left[\frac{1}{0.08} - \frac{10}{\left(1 + 0.08\right)^{10} - 1}\right] \approx 6{,}936

Symbols and units

SymbolMeaningUnit
AeqA_{\text{eq}}equivalent annual cost$/year
AbaseA_{\text{base}}first-year base cost$/year
GGannual arithmetic increase$/year
iidiscount rate—
nnnumber of end-year costsyear

Related calculators

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