Finance

Compound Interest Calculator

See how savings or investments can grow when interest is added to the balance and then earns interest itself — compound growth over time.

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Result

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The formula

The future value of a lump sum with compound interest is principal times one plus the periodic rate, raised to the number of compounding periods. More frequent compounding at the same nominal APR produces a slightly higher effective annual yield (APY).

A = P(1 + r/n)^(n·t)

Worked example

  1. P = $10,000, r = 5% (0.05), n = 12 monthly compounds, t = 10 years
  2. A = 10000 × (1 + 0.05/12)^(12×10) = 10000 × (1.004166…)^120
  3. A ≈ $16,470

Result: Final balance ≈ $16,470 (interest ≈ $6,470)

How compound interest is calculated

Compounding reinvests earned interest so later periods earn on a larger base. The formula below assumes a fixed rate and no extra deposits or withdrawals.

Variables

P is the starting principal. r is the nominal annual rate as a decimal (5% → 0.05). n is compounds per year (12 = monthly, 365 ≈ daily). t is time in years. A is the ending amount.

APR vs APY (EAR)

APR is the quoted nominal annual rate. APY (or effective annual rate) includes compounding: APY = (1 + r/n)^n − 1. Compare savings products on APY when compounding frequencies differ.

What this tool omits

Regular monthly contributions, fees, taxes, and changing rates need a different schedule (or an amortization-style model). Inflation reduces real purchasing power even when the nominal balance rises.

Interesting facts

Growth on growth

Compound interest earns returns on prior interest. Over long horizons the curve bends upward compared with simple interest on the original principal alone.

Time usually beats late heroics

Starting earlier with smaller amounts often beats larger deposits started years later because more compounding periods apply.

APR vs APY

APR states the nominal annual rate; APY folds in compounding frequency so products can be compared fairly.

Frequency matters a little

Daily or monthly compounding grows slightly faster than annual compounding at the same nominal APR — the gap widens over decades.

Inflation is the silent partner

A 7% nominal return with 3% inflation is closer to 4% real growth. Ask what purchasing power you keep.

Frequently asked questions

Interest calculated on both the original principal and interest already added in prior periods — growth on growth.

Use A = P(1 + r/n)^(n·t). Enter principal, annual rate, years, and compounds per year; the calculator evaluates the formula for you.

At the same nominal APR, yes slightly — because interest is added more often. Always compare APY when shopping products.

No. This page models a single principal left to compound. For contribution schedules, use a savings-goal style plan or spreadsheet.

No. Market returns vary; this is fixed-rate mathematics for illustration, not a forecast.

References

  1. Compound interest — consumer explanation — U.S. Securities and Exchange Commission (Investor.gov) Plain-language definition for investors.
  2. Truth in Savings (APY disclosure context) — Consumer Financial Protection Bureau US framework for savings yield disclosures (APY).
  3. Interest rate mathematics overview — Federal Reserve Education Educational background on rates and compounding concepts.