The compound interest formula is the single equation behind every savings, investment, and loan projection on this site. It is not a proprietary or vendor-specific calculation — it is standard time-value-of-money mathematics taught in introductory finance and used by regulators such as the U.S. Securities and Exchange Commission in their investor education materials.

The Formula

For a lump sum compounded at a fixed nominal rate:

A = P(1 + r/n)^(nt)

What each variable means

  • •**A** = the future amount (principal + accumulated interest).
  • •**P** = the principal, the starting amount you invest or deposit.
  • •**r** = the annual nominal interest rate written as a decimal (7% becomes 0.07).
  • •**n** = the number of times interest is compounded per year (12 for monthly, 365 for daily, 1 for annual).
  • •**t** = the number of years the money is invested.

Where does it come from? Each compounding period, the balance is multiplied by (1 + r/n). Over nt total periods that factor is applied nt times, hence the exponent. The formula is the closed-form solution of that repeated multiplication. (See the SEC Investor.gov compound interest explainer and calculator: investor.gov.)

Worked Example You Can Verify

Start with P = $1,000, invest at r = 7% (0.07) compounded monthly (n = 12) for t = 10 years:

  1. Compute the periodic rate: r/n = 0.07 / 12 = 0.0058333.
  2. Compute the number of periods: nt = 12 × 10 = 120.
  3. Raise the factor: (1.0058333)^120 ≈ 2.00965.
  4. Multiply by principal: A = 1000 × 2.00965 ≈ $2,009.65.

So $1,000 grows to about $2,009.65 in 10 years at 7% compounded monthly — roughly doubling, consistent with the Rule of 72 (72 ÷ 7 ≈ 10.3 years to double).

Adding a Recurring Monthly Contribution

Most real plans add money on a schedule. The future value of a lump sum plus a recurring contribution is the sum of two real formulas:

A = P(1 + r/n)^(nt) + PMT × [ ((1 + r/n)^(nt) − 1) / (r/n) ]

where PMT is the amount added each compounding period. With the same $1,000 lump sum plus $100 contributed every month for 10 years at 7%: the contribution side grows to about $17,308, so the total future value is approximately $19,318 (you contributed $13,000 total, and about $6,318 is interest). You can confirm this with our compound interest calculator.

The Continuous-Compounding Variant

When interest is compounded at every instant, n approaches infinity and the formula becomes A = P·e^(rt), where e ≈ 2.71828. For the same $1,000 at 7% for 10 years: A = 1000 × e^(0.7) ≈ $2,013.75. Continuous compounding is only marginally more than daily compounding — the frequency matters far less than the rate and time.

Step-by-Step: Calculate Compound Interest Yourself

  1. Write down P, the annual rate as a decimal (r), n (frequency), and t (years).
  2. Divide r by n to get the periodic rate.
  3. Multiply n by t to get the total number of periods.
  4. Calculate (1 + periodic rate) raised to the total periods.
  5. Multiply by P for a lump sum; add the contribution term above if you also save regularly.
  6. Sanity-check against the Rule of 72 and against our calculator.

Note on vendor-specific parameters: a generic compound-interest or annuity formula is pure mathematics and does not depend on any bank, broker, fund, or product "tuning" parameters. There are no manufacturer- or vendor-specific coefficients to enter — only the universal variables (principal, rate, time, frequency, contribution). Product-specific terms (fees, APY caps, promotional rates) belong on the provider's disclosure, not in the formula.

<strong>Disclaimer:</strong> The content provided on CompoundFig is for educational and informational purposes only and does not constitute financial, tax, legal, or investment advice. All calculations and projections are hypothetical and based on assumed rates of return, which may not reflect actual market conditions. Historical figures cited here are factual records, not forecasts or guarantees of future performance. Individual results will vary. Consult a qualified financial professional before making decisions. CompoundFig does not provide personalized financial recommendations.

Sources & References

  • •U.S. Securities and Exchange Commission (Investor.gov) — Compound Interest calculator and investor education: investor.gov
  • •Standard time-value-of-money formula (introductory corporate finance); the closed-form A = P(1 + r/n)^(nt) is derived from repeated periodic multiplication.