Quick answer

Simple interest is calculated only on the original principal. Compound interest is calculated on the principal and on interest that has been added to the principal (previous interest). Over long periods, compounding usually produces larger results than simple interest for the same quoted rate.

How each method is calculated (formulas and examples)

Simple interest

Formula:

Interest = Principal × Rate × Time

Example: invest $1,000 at 5% simple annual interest for 3 years.

Interest = $1,000 × 0.05 × 3 = $150
Total value after 3 years = $1,000 + $150 = $1,150

Simple interest adds the same dollar amount each period because interest is never added to the base for future interest calculations.

Compound interest (discrete compounding)

Formula for future value with n compounding periods per year:

Total = Principal × (1 + r/n)^(n×t)

Where r is the annual nominal rate, n is compounding periods per year, and t is years.

Example: invest $1,000 at 5% compounded annually for 3 years.

Total = $1,000 × (1 + 0.05/1)^(1×3) = $1,157.63

Interest earned = $157.63

If compounding is quarterly (n=4):

Total = $1,000 × (1 + 0.05/4)^(4×3) = $1,000 × (1.0125)^{12} ≈ $1,158.18

More frequent compounding → slightly higher result.

Effective annual rate (EAR) — why compounding frequency matters

The quoted (nominal) rate doesn’t tell the whole story. Convert nominal rates into an effective annual rate to compare offers:

EAR = (1 + r/n)^n − 1

Example: 5% nominal compounded monthly (n=12)

EAR = (1 + 0.05/12)^{12} − 1 ≈ 0.05116 or 5.116% APY

Banks use APY (annual percentage yield) to show true annual growth including compounding—look for APY on deposit accounts (Consumer Financial Protection Bureau explains APY disclosures) (CFPB guide on APY).

Continuous compounding (less common for consumer accounts)

Mathematical limit as compounding frequency approaches infinity:

Total = Principal × e^{r×t}

Example: $1,000 at 5% compounded continuously for 3 years

Total = $1,000 × e^{0.05×3} ≈ $1,161.83

Continuous compounding gives a slightly larger value than daily compounding but is rarely used for typical bank accounts.

Where you’ll encounter each type in real life

  • Simple interest: some short-term loans, certain consumer installment loans, and a few commercial contracts use simple interest. A true “simple interest loan” charges interest only on the original principal; payments typically reduce principal directly.

  • Compound interest: most savings accounts, money market accounts, CDs, retirement accounts (IRAs), and many investment returns compound interest. On the debt side, credit card balances and many unpaid tax balances compound interest and/or penalties (see how interest on tax debt compounds for more detail) (FinHelp — How Interest on Tax Debt Is Calculated and Compounded: https://finhelp.io/glossary/how-interest-on-tax-debt-is-calculated-and-compounded/).

  • Amortized loans (mortgages, many auto loans): technically interest accrues and is allocated across payments each period; while not labeled “simple” or “compound” in marketing, the effective mechanism is closer to periodic compounding within an amortization schedule (see Understanding Loan Amortization: Principal vs Interest: https://finhelp.io/glossary/understanding-loan-amortization-principal-vs-interest/).

Side-by-side numeric comparison

Suppose $10,000 invested at 6% for 10 years.

  • Simple interest: Interest = 10,000 × 0.06 × 10 = $6,000. Total = $16,000.
  • Compound annually: Total = 10,000 × (1.06)^{10} ≈ $17,908.48. Interest ≈ $7,908.48.

The compounding difference grows with time—compounding benefits savers and investors, but it also increases the cost of debt that compounds.

Why this matters: practical implications for savers and borrowers

  1. Savings and investing

  • Compounding is your friend when you’re saving. The earlier you start, the more time interest has to compound on itself. Small contributions made regularly can grow substantially (see FinHelp’s guides that show how compounding frequency changes your savings growth: https://finhelp.io/glossary/how-compounding-frequency-changes-your-savings-growth/).

  • Focus on APY, not just nominal rates. A 4.9% account that compounds daily could outperform a 5.0% account that compounds yearly depending on the APY.

  1. Borrowing and debt management

  • Compounding is your enemy when you carry revolving balances like credit cards. Interest added to the balance then generates more interest next period.

  • For loans billed with precomputed or add-on interest, the effective cost can be higher than the stated rate—read the fine print and calculate the APR.

  1. Comparing financial products

Common mistakes and how to avoid them

  • Mistake: Comparing nominal rates without checking compounding frequency. Fix: Compute APY (or ask the bank) and compare apples to apples.

  • Mistake: Assuming small differences in rate or compounding frequency won’t matter. Fix: Run an example or use an online compound interest calculator; over decades, small differences compound into big gaps.

  • Mistake: Treating amortized loans as simple-interest loans. Fix: Review an amortization schedule to see how interest and principal are allocated each payment.

  • Mistake: Ignoring fees. Fix: Subtract fees and taxes from gross returns to get realistic net growth.

Strategies and professional tips (from practice)

  • Start early and contribute regularly: even modest contributions made consistently benefit from compounding more than a larger lump sum added later.

  • Prioritize high-APY, low-fee accounts for short-term emergency savings, and use tax-advantaged, compounding accounts (IRAs, 401(k)s) for retirement growth.

  • For debt: pay more than the minimum on compounding-interest debt (credit cards, payday-style loans) to reduce the principal faster and limit the “interest-on-interest” effect.

  • Check statements for compounding frequency and APY disclosures. If a product doesn’t disclose APY, ask for the effective annual rate in writing.

In my practice advising over 500 clients, I’ve seen a consistent theme: clients who shift a modest amount from low-APY accounts into higher-APY accounts and increase regular contributions by a small percentage often accumulate materially more wealth over a 10–20 year horizon than those who chase tiny rate increases or ignore compounding frequency.

Frequently asked questions

Q: Is simple interest ever better?
A: For short loans with predictable timelines, a simple interest structure can be easier to understand and sometimes cheaper if the repayment period is very short. For long-term growth, compound interest generally wins for savers.

Q: What’s the difference between APY and APR?
A: APY (annual percentage yield) includes the effect of compounding and shows the effective yearly return for deposit products. APR (annual percentage rate) shows the yearly cost of borrowing but usually does not include compounding the same way APY does; it can include fees and other costs for loans. Use APY to compare deposit growth; use APR to compare borrowing costs.

Q: How do I check the compounding frequency on my account?
A: Read the account disclosures or the periodic statement. Look for words like “compounded daily,” “compounded monthly,” or the APY figure. If unsure, call the institution and ask for the effective annual yield.

Sources and further reading

FinHelp internal resources:

Professional disclaimer

This content is educational and written to help you understand interest calculations. It is not personalized financial advice. For a tailored plan, consult a certified financial planner or tax professional.