Compound Interest

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.