Compound Interest Calculator — Formula and Worked Examples

Compound interest is often summarized as “interest on interest.” That slogan is directionally right, but the formula makes the assumptions visible: a fixed rate, a fixed schedule, and usually no deposits, withdrawals, or fees. Those assumptions are why a Compound Interest Calculator is excellent for learning and rough comparisons — and why it is not a forecast of investment returns.

This article explains the standard formula with worked numbers. It is educational mathematics, not financial, investment, or tax advice. Nothing here guarantees future performance. Review the Disclaimer.

The standard formula

A = P × (1 + r/n)^(n × t)

| Symbol | Meaning | |--------|---------| | A | Estimated future value | | P | Starting principal | | r | Annual nominal rate (decimal; 5% → 0.05) | | n | Compounding periods per year | | t | Time in years |

Interest earned ≈ A − P.

Worked example — annual compounding

P = 5,000, r = 0.06, n = 1, t = 3:

A = 5000 × (1.06)^3 = 5000 × 1.191016 ≈ 5,955.08

Interest ≈ 955.08.

Same rate, monthly compounding

Keep P, r, and t; set n = 12:

A = 5000 × (1 + 0.06/12)^36 = 5000 × (1.005)^36 ≈ 5,983.40

About $28 more than annual compounding in this illustration — not magic, just more frequent addition of interest to the base.

Why frequency matters (and when it does not)

At modest rates and short horizons, frequency differences look small. Over longer horizons they widen. When comparing real savings products, marketing may quote APR vs APY; APY already folds compounding into an effective yearly yield. Compare like with like.

Compound vs simple interest

Simple interest uses I = P × r × t and does not grow the base. The same 5,000 at 6% for 3 years simple:

I = 5,000 × 0.06 × 3 = 900 → total 5,900.

That is less than either compound scenario above. Explore both with the Simple Interest Calculator and the compound tool side by side.

Linking CAGR and compound interest

If you already know beginning and ending values, CAGR asks: “What constant annual rate connects these two points?” Compound interest asks the forward question: “If rate and frequency are fixed, where does principal land?” They are cousins — neither predicts tomorrow’s market.

Assumptions that break in real life

• Rates change
• Fees and taxes reduce balances
• Contributions and withdrawals alter principal
• Investments can lose value

A spreadsheet that compounds a fantasy 12% for 40 years can print a huge number. That number is not a promise.

Using the calculator well

1. Enter principal and annual percent rate.
2. Set years honestly (months → fractional years if needed).
3. Match compounding to the example you are studying.
4. Change one input at a time when comparing scenarios.

Limitations

Calculator outputs are constant-rate educational estimates. They are not lender quotes, portfolio projections, or advice. For decisions about saving or investing, consult a qualified professional and read product disclosures. Full terms: disclaimer.

When the goal is intuition — how rate, time, and frequency interact — run two or three scenarios in the Compound Interest Calculator and write down the assumptions next to each result.