What are the simple and compound interest formulas, and how do their results differ?

The simple interest formula uses only the original principal, while the compound interest formula also applies interest to prior interest. Their paths start close and diverge as rate, frequency and time increase.

Simple and compound interest formulas

Simple = Principal × (1 + Rate ÷ 100 × Years)Compound = Principal × (1 + Rate ÷ 100 ÷ n)^(n × Years)Difference = Compound − Simple

Two interest methods on one balance

The default comparison applies one principal, annual rate and term to both methods. It reports each ending amount and the extra growth created by compounding.

Illustrative inputs; currency amounts below use USD. Rates and prices are assumptions, not live quotes.

Principal
$10,000.00
Annual rate
7%
Years
20
Compounds per year
12

Step-by-step calculation

  1. Simple balance = 10,000 × (1 + 7 ÷ 100 × 20) = 24,000.
  2. Compound balance = 10,000 × (1 + 7 ÷ 100 ÷ 12)^(12 × 20) = 40,387.38849.
  3. Compounding advantage = 40,387.38849 − 24,000 = 16,387.38849 over the same term, rate and starting balance.

Intermediate figures are rounded for reading. Results use the full calculation precision.

Compounding is worth$16,387.39
With compounding$40,387.39
With simple interest$24,000.00
Compound interest earned$30,387.39

Locating the interest-on-interest difference

The difference is the interest-on-interest effect. With a short term or low rate it may be small; repeated compounding over many periods makes it more visible.

Matching units and compounding frequency

The two results are comparable only when rate and term use the same units. Compounding frequency must also match the formula rather than being assumed.

  • Principal, annual rate and term are identical in both cases.
  • Compound frequency follows the input and displayed equation.
  • Deposits, withdrawals, tax and fees are excluded.

Calculations related to simple vs compound interest

The following tools examine neighbouring parts of the same calculation without changing the inputs or assumptions used above.

References

Sources and conventions

Quick answers

Frequently asked questions

What is the simple interest formula?

Ending value equals principal multiplied by one plus the annual rate multiplied by the number of years.

What is the compound interest formula?

Ending value equals principal multiplied by one plus the periodic rate, raised to the total number of compounding periods.

Why does compound interest usually exceed simple interest?

Compound interest earns returns on earlier interest, while simple interest continues to use only the original principal.

How does compounding frequency change the result?

The annual rate is divided and applied more often, which changes the effective growth over the term.

Calculation method and limitations · Report an error

Educational content only. This guide is not financial advice.