Interest Calculator Compare simple, compound, and continuous interest — with formulas, visualizations, and real-world exa...
Interest Calculator
Compare simple, compound, and continuous interest — with formulas, visualizations, and real-world examples.
Simple Interest
$$A = P(1 + rt)$$ • $P$ = Principal • $r$ = Annual rate (decimal) • $t$ = Time in years
Used for: short-term loans, Treasury bills, HELOC draw periods.
Compound Interest
$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ • $n$ = Compounding periods/year (12 = monthly)
Used for: savings accounts, CDs, mortgages, most investments.
Continuous Compounding
$$A = Pe^{rt}$$ • $e$ = Euler’s number (~2.71828)
Theoretical max — banks approach this with daily compounding.
Same $10,000 at 5% for 10 years:
- Simple: $15,000
- Annually: $16,289
- Monthly: $16,470
- Daily: $16,486
- Continuous: $16,487
✅ **Key Insight**: Frequency has diminishing returns. Going from annual to monthly gains ~$180; monthly to daily adds only ~$16.
⚠️ Banks quote **nominal rate** (e.g., “5% APY”), but actual growth depends on compounding. Always compare **APY** (Annual Percentage Yield), not APR.
Quick mental math for investors:
- Rule of 72: Years to double = 72 ÷ annual return (%) • 6% return → 12 years to double • 8% → 9 years
- Rule of 114: Years to triple = 114 ÷ annual return (%) • 6% → 19 years to triple • 8% → 14.25 years
Accuracy: Works best for 4%–12% returns. For 5%: • Actual doubling: 14.21 years • Rule of 72: 14.4 years → **0.19-year error**.
➡️ Simple Interest
Ideal for estimating short-term loan costs or T-bill returns.
➡️ Compound Interest
Model savings, CDs, or investments — choose daily/monthly compounding.
➡️ Continuous Compounding
See the mathematical limit — useful for academic or high-frequency scenarios.
Note: All calculations assume constant rate and no taxes/fees.