Exemples
Intérêts composés — Worked Examples
5 real worked examples for the Intérêts composés calculator. See how we solve common scenarios with full step-by-step math.
Long-term retirement growth
Scénario
A 25-year-old invests $500/month at 7% annual return, compounded monthly, until age 65 (40 years).
Entrées
- Monthly contribution
- $500
- Annual return
- 7%
- Compounding
- monthly
- Years
- 40
Étapes du calcul
- Monthly rate: 0.07 / 12 = 0.00583
- Number of periods: 40 × 12 = 480
- FV = 500 × [((1.00583)⁴⁸⁰ − 1) / 0.00583]
- FV = 500 × [1427.5 / 0.00583] — wait, let me redo:
- FV = 500 × [(1.00583)⁴⁸⁰ − 1] / 0.00583
- FV ≈ 500 × 2738.6
- FV ≈ $1,369,300
Résultat
Future value: $1,369,300 • Of which contributions: $240,000, growth: $1,129,300
Lump-sum investment
Scénario
A one-time $10,000 investment at 6% annual return, compounded annually, for 30 years.
Entrées
- Initial
- $10,000
- Annual return
- 6%
- Compounding
- annually
- Years
- 30
Étapes du calcul
- A = 10000 × (1.06)³⁰
- A = 10000 × 5.7435
- A ≈ $57,435
Résultat
Future value: $57,435 (5.7× growth) • Interest earned: $47,435
High-yield savings
Scénario
$25,000 in a savings account at 4.5% APY, compounded daily, for 5 years.
Entrées
- Principal
- $25,000
- APY
- 4.5%
- Compounding
- daily
- Years
- 5
Étapes du calcul
- Daily rate: 0.045 / 365 = 0.000123
- Periods: 5 × 365 = 1825
- A = 25000 × (1.000123)¹⁸²⁵
- A = 25000 × 1.2523
- A ≈ $31,308
Résultat
Future value: $31,308 • Interest earned: $6,308 over 5 years
Doubling time with Rule of 72
Scénario
How long to double $1,000 at 8% annual return?
Entrées
- Principal
- $1,000
- Annual return
- 8%
Étapes du calcul
- Rule of 72: Years to double ≈ 72 / rate
- 72 / 8 = 9 years
- Verify with formula: A = 1000 × (1.08)⁹
- A = 1000 × 1.999 = $1,999 ✓
Résultat
Doubling time: 9 years. Rule of 72 is accurate for 5-12% rates. For higher rates, use 69.3 / r × ln(2) for precision.
Inflation erosion of purchasing power
Scénario
How much will $100,000 be worth in 20 years at 3% annual inflation?
Entrées
- Today's value
- $100,000
- Inflation rate
- 3%
- Years
- 20
Étapes du calcul
- Real value = 100000 / (1.03)²⁰
- Real value = 100000 / 1.8061
- Real value ≈ $55,367
Résultat
$100K today buys the same as $55,367 in 20 years. Inflation cuts purchasing power in half every ~24 years at 3%.