ClueLuma

Initial plus annual accumulation calculator

Future accumulated fund is calculated as P × (1+i)^n + A × [(1+i)^n−1]/i. Use the stated system boundary and matching input units.

F=P×(1+i)n+A×[(1+i)n−1]iF = P \times \left(1 + i\right)^{n} + \frac{A \times \left[\left(1 + i\right)^{n} - 1\right]}{i}

Calculator

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

$
$/year
—
year
$

Worked example

Given

  • PP = 10,000 $
  • AA = 5,000 $/year
  • ii = 0.05 —
  • nn = 10 year
F=10,000×(1+0.05)10+5000×[(1+0.05)10−1]0.05≈79,178F = 10{,}000 \times \left(1 + 0.05\right)^{10} + \frac{5000 \times \left[\left(1 + 0.05\right)^{10} - 1\right]}{0.05} \approx 79{,}178

Symbols and units

SymbolMeaningUnit
FFfuture accumulated fund$
PPinitial reserve$
AAequal year-end deposits$/year
iicompound interest rate—
nnnumber of yearsyear

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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.