Simple vs Compound Interest — Side-by-Side

Enter your values and compare totals instantly. We’ll also plot a small chart so you can see the difference over time.

Enter your values

Starting amount you deposit or borrow.
Months/days are converted to years for the formulas.

Results

Enter values and click Compare to see totals, differences, and EAR.

Learn: Simple vs Compound Interest

This section explains when each model is used, the exact formulas, and how banks in different regions refer to rates (UK: AER, US: APY, general: EAR). Everything here is simplified and for education only.

Quick definitions

  • Simple interest: interest grows linearly with time. Often used in short-term loans or straightforward agreements.
  • Compound interest: interest earns interest. Growth accelerates with more frequent compounding (monthly, daily, continuous).

Formulas at a glance

  • Simple total: \( A_{\text{simple}} = P(1 + r t) \)
  • Compound (discrete): \( A_{\text{comp}} = P\left(1 + \frac{r}{n}\right)^{n t} \)
  • Compound (continuous): \( A_{\text{cont}} = P\,e^{r t} \)
  • Effective Annual Rate (EAR): \( \text{EAR} = \left(1 + \frac{r}{n}\right)^n - 1 \) (continuous: \( e^{r} - 1 \))

Worked example (side-by-side)

Suppose P = £10,000, APR r = 5%, t = 3 years, compounding monthly (n = 12):

  • Simple: \( A = 10{,}000 \times (1 + 0.05 \times 3) = \) £11,500.00
  • Compound (monthly): \( A = 10{,}000 \times \left(1 + \frac{0.05}{12}\right)^{36} \approx \) £11,614.72
  • Extra from compounding vs simple over 3 years: ~£114.72
  • EAR for 5% nominal, monthly compounding: \( (1 + 0.05/12)^{12} - 1 \approx \) 5.116%

GEO notes (UK / US / EU naming)

  • UK: Savings are commonly advertised with AER (Annual Equivalent Rate) — an “effective” yearly rate including compounding. Mortgages often calculate interest daily but are paid monthly; lenders still quote a nominal APR.
  • US: Deposit accounts use APY (similar to EAR/AER). Loans/credit cards quote a nominal APR; the effective cost depends on compounding and fees.
  • General: When comparing offers, convert to an effective rate (EAR/APY/AER) so the compounding frequency is accounted for.

When each model makes sense

  • Use simple interest for short, fixed-term agreements where compounding isn’t stipulated (some notes, quick estimates, educational contexts).
  • Use compound interest for most savings accounts, investment growth, credit cards, and typical amortising loans/mortgages (compounding frequency matters).

Common pitfalls

  • Mixing units: ensure time \(t\) is in years (months ÷ 12; days ÷ 365).
  • Comparing nominal APRs only: two 5% APR offers can have different outcomes if one compounds monthly and another daily.
  • Ignoring fees/taxes/inflation: this calculator doesn’t model fees, tax treatment, or inflation. Real return ≈ nominal return − inflation (rough rule).
  • Assuming compounding you don’t have: read the product terms — some contracts are simple interest or compound at unusual intervals.

Disclaimer: Educational illustration only. Not financial advice. Always check your provider’s terms (compounding method, fees, and disclosure standard such as APR/APY/AER).

Explore more tools