Beispiele
Hypothek — Worked Examples
3 real worked examples for the Hypothek calculator. See how we solve common scenarios with full step-by-step math.
Standard 30-year fixed mortgage
Szenario
A $400,000 home, 20% down ($80,000), financed at 6.5% APR for 30 years.
Eingaben
- Home price
- $400,000
- Down payment
- $80,000 (20%)
- Loan amount
- $320,000
- APR
- 6.5%
- Term
- 30 years
Berechnungsschritte
- P = $320,000
Loan principal.
- r = 0.065 / 12 = 0.005417
Monthly rate.
- n = 30 × 12 = 360
Number of payments.
- M = 320000 × (0.005417 × 1.005417³⁶⁰) / (1.005417³⁶⁰ − 1)
- M ≈ $2,023 / month
Ergebnis
Monthly P&I: $2,023 • Total interest paid: $408,160 over 30 years
15-year mortgage comparison
Szenario
Same $320,000 loan, 6.5% APR, but 15-year term.
Eingaben
- Loan amount
- $320,000
- APR
- 6.5%
- Term
- 15 years
Berechnungsschritte
- P = $320,000
- n = 180
- M = 320000 × (0.005417 × 1.005417¹⁸⁰) / (1.005417¹⁸⁰ − 1)
- M ≈ $2,795 / month
Ergebnis
Monthly P&I: $2,795 (higher) • Total interest: $183,108 (much lower) — saves $225,052 vs. 30-year
Refinancing break-even
Szenario
Current 7% APR, refinancing to 5.5% APR on $250,000 balance, 30-year remaining. Closing costs: $5,000.
Eingaben
- Current APR
- 7%
- New APR
- 5.5%
- Balance
- $250,000
- Closing costs
- $5,000
Berechnungsschritte
- Current payment: 250000 × (0.00583 × 1.00583³⁶⁰) / (1.00583³⁶⁰ − 1) ≈ $1,664
- New payment: 250000 × (0.00458 × 1.00458³⁶⁰) / (1.00458³⁶⁰ − 1) ≈ $1,420
- Monthly savings: $244
- Break-even: $5,000 / $244 ≈ 20.5 months
Ergebnis
Monthly savings: $244 • Break-even point: ~21 months. Refi pays off in <2 years.