Simple versus compound interest

Ask what earns the next interest amount

Principal is the money on which interest is calculated. Under a simple-interest model with an unchanged principal, each equal time period earns the same amount. Under compounding, credited interest stays in the balance and can earn further interest.

That difference is easier to understand by following the balance than by comparing product names. A savings account can have a nominal annual rate, a compounding frequency, rules about when interest is credited and restrictions on withdrawals. Read all of them before choosing a formula. The Investor.gov definition of compound interest identifies principal and accumulated interest as the two parts.

Use matching rate and time units

With unchanged principal P, annual rate r as a decimal and time t in years, simple interest is P × r × t. Final amount is P × (1 + r × t). A 5% input becomes r = 0.05.

With no contributions or withdrawals, compound final amount is P × (1 + r/m)^mt, where m is the number of compounding periods per year and r is a nominal annual rate. Annual compounding uses m = 1; monthly uses m = 12. Do not divide an effective annual yield by 12 as though it were the same nominal input.

These formulas describe the selected conventions. Actual daily accrual needs the contract's day-count basis, dates and balances.

Keep the comparison controlled

Assume 1,000.00, a 5% nominal annual rate, three complete years, no fees and no money moving in or out. Compare simple interest with annual compounding.

On a narrow screen, scroll the table horizontally to see all columns.

The compound balance is 1,157.625 before display rounding. The final displayed difference is 7.63. It comes from applying the rate to earlier interest, not from depositing more money. The CFPB compound-interest explainer describes this mechanism.

A deposit is not investment growth

If you add 100.00 in the last month, that deposit has less time to grow than the original balance. Adding every planned contribution to principal and compounding the whole amount from day one exaggerates growth.

A useful result separates initial principal, later contributions and growth. It also says whether contributions occur at the start or end of each period. End-of-month deposits are a clear convention for a monthly model, but they cannot reproduce irregular bank transactions exactly. Model compound growth with a regular contribution schedule, or use the savings-goal calculator to work backwards from a target.

Compare rates on a consistent basis

A nominal 12% compounded monthly means 1% per month. Leaving the interest invested gives an effective annual rate of (1.01¹² − 1) × 100 = 12.682503…%. That is different from 12% compounded once a year.

The Microsoft EFFECT documentation describes the nominal-to-effective conversion. It does not turn a generic effective rate into a legally compliant APR or advertised savings disclosure. Product charges and mandated conventions can change the relevant comparison.

Choose the model that matches the money

Use simple interest for an unchanged principal only when that is the intended method. Use a compound model for interest reinvested into the balance. Use amortization for a repayment loan whose principal falls after payments. A credit card may need daily balances and several APR categories rather than any single annual formula.

Keep nominal growth separate from purchasing power: a balance growing by 5% with prices rising by 3% does not gain 5% in real spending capacity. Check fees and taxes separately. No constant-return illustration establishes what an investment will earn in the future.