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Compound Interest

Future Value
Present Value (PV)
Annual Rate % (APR)
Years (t)
Compounding
Contribution per period (PMT)
Future Value
47526.55
Total contributions
24000
Interest earned
13526.55
Options
Display
Display only; internal calculations use full precision.

About Compound Interest

Compute future value, required present value, required periodic contribution (PMT), or periods (N) under nominal APR with discrete compounding. Continuous compounding is supported for single lump-sum growth: FV = PV · e^{r·t}.

Formulas (discrete compounding, rate per period i = APR/m, N = m·t)

  • FV = PV·(1+i)N + PMT·[((1+i)N − 1)/i]·K, where K=1 for end, K=(1+i) for beginning.
  • PV = [FV − PMT·[((1+i)N − 1)/i]·K] / (1+i)N.
  • PMT = [FV − PV·(1+i)N] / {[((1+i)N − 1)/i]·K}.
  • N: let A=PMT·K, then (1+i)N = (FV + A/i) / (PV + A/i), so N = ln(·)/ln(1+i).

When i=0 (zero rate), formulas reduce to linear sums (e.g., FV=PV+PMT·N). Negative or extreme values can be invalid.