Finance calculators

Compound interest calculator

Free compound interest calculator with regular contributions, daily to annual compounding, effective annual rate and a year-by-year growth chart.

Inputs

Initial amountInterest rate%YearsyearsCompoundingRegular contributionContribution frequencyContributions paid at

Results

Methodology

Conventions

Interest compounds m times a year at the nominal rate r.
Contributions are paid p times a year, at the start or end of each period; between contributions the balance grows at the equivalent periodic rate j.

References

Kellison, The Theory of Interest, ch. 3 and 5

Formulas

Equivalent periodic rate: j = (1 + r/m)^{m/p} - 1
Lump sum: FV_0 = P (1 + r/m)^{m t}
Contributions: FV_c = C \cdot \frac{(1 + j)^{p t} - 1}{j} \cdot (1 + j)^{\delta},\ \delta = 1 \text{ if paid at start}
Effective annual rate: EAR = (1 + r/m)^m - 1