Personal Finance · 5 min read
How to Calculate Compound Interest
Interest on interest — A = P(1 + r/m)^{mt}
Compound interest reinvests earned interest into the balance, so later periods earn interest on interest. This tutorial walks through A = P(1 + r/m)^{mt}, a $5,000 / 4% / 10-year monthly worked example, and a playground that compares compound growth with simple interest. Figures are illustrative; fees and taxes are omitted.
Written by the My Calculator Stack editorial team. About our methods
These figures are illustrative. Fees, taxes, and product-specific rules are omitted. This is not investment, tax, or financial advice.
1.What compound interest is
Compound interest adds each period’s interest back into the principal before the next period runs. Simple interest does not — it stays linear in time (I = Prt). Savings accounts, CDs, and many loans quote a nominal annual rate r with m compounding periods per year. More frequent compounding raises the future value slightly at the same nominal rate. This page assumes a single deposit and no extra contributions.
2.The formula
Future value is A = P(1 + r/m)^{mt}. P is the principal, r is the nominal annual rate as a decimal (4% → 0.04), m is compounds per year, and t is years. The period rate is r/m; the exponent mt is the number of periods. Interest earned is A − P. The same equation powers the compound interest calculator on this site.
\[ A = P\left(1+\frac{r}{m}\right)^{mt} \]
3.Worked example
Take $5,000 at 4% annual for 10 years, compounded monthly (m = 12) — the same defaults as the compound interest calculator. Period rate r/m = 0.04/12, and mt = 120 periods. Then A = 5000 × (1 + 0.04/12)^{120} ≈ $7,454. Interest earned ≈ $2,454. Simple interest on the same P, r, and t is I = 5000 × 0.04 × 10 = $2,000, so the simple total is $7,000. The gap is interest earned on previously credited interest.
\[ A=5000\left(1+\frac{0.04}{12}\right)^{120}\approx 7454 \]
4.Growth versus simple interest
Move principal, rate, years, and compounds per year to see compound future value update beside a simple-interest total at the same P, r, and t. The bars share one scale so the compounding gap is visible. This is a teaching widget — no extra deposits, no fees, no full calculator chrome. Open the compound interest calculator when you want the standalone tool.
Inline playground
Illustrative — fees and taxes omitted
Compound future value
$7,454.16
Simple total: $7,000.00 · gap $454.16
5000 × (1 + 0.04/12)^120 ≈ 7454.16
Illustrative only — a single deposit, no extra contributions, no fees or taxes.
Open the full compound interest calculator →5.Open the full calculator
The compound interest calculator uses the same A = P(1 + r/m)^{mt} equation, the same $5,000 / 4% / 10-year monthly example, and the same limitation that taxes and fees are omitted. Browse other personal finance tools if you need simple interest, a loan payment, or an amortization schedule next.
Try it yourself
Open the related calculator and put these formulas to work.