Esempi

Mutuo — Worked Examples

5 real worked examples for the Mutuo calculator. See how we solve common scenarios with full step-by-step math.

1

Standard 30-year fixed mortgage

Scenario

A $400,000 home, 20% down ($80,000), financed at 6.5% APR for 30 years.

Input

Home price
$400,000
Down payment
$80,000 (20%)
Loan amount
$320,000
APR
6.5%
Term
30 years

Passaggi del calcolo

  1. P = $320,000

    Loan principal.

  2. r = 0.065 / 12 = 0.005417

    Monthly rate.

  3. n = 30 × 12 = 360

    Number of payments.

  4. M = 320000 × (0.005417 × 1.005417³⁶⁰) / (1.005417³⁶⁰ − 1)
  5. M ≈ $2,023 / month

Risultato

Monthly P&I: $2,023 • Total interest paid: $408,160 over 30 years

2

15-year mortgage comparison

Scenario

Same $320,000 loan, 6.5% APR, but 15-year term.

Input

Loan amount
$320,000
APR
6.5%
Term
15 years

Passaggi del calcolo

  1. P = $320,000
  2. n = 180
  3. M = 320000 × (0.005417 × 1.005417¹⁸⁰) / (1.005417¹⁸⁰ − 1)
  4. M ≈ $2,795 / month

Risultato

Monthly P&I: $2,795 (higher) • Total interest: $183,108 (much lower) — saves $225,052 vs. 30-year

3

Refinancing break-even

Scenario

Current 7% APR, refinancing to 5.5% APR on $250,000 balance, 30-year remaining. Closing costs: $5,000.

Input

Current APR
7%
New APR
5.5%
Balance
$250,000
Closing costs
$5,000

Passaggi del calcolo

  1. Current payment: 250000 × (0.00583 × 1.00583³⁶⁰) / (1.00583³⁶⁰ − 1) ≈ $1,664
  2. New payment: 250000 × (0.00458 × 1.00458³⁶⁰) / (1.00458³⁶⁰ − 1) ≈ $1,420
  3. Monthly savings: $244
  4. Break-even: $5,000 / $244 ≈ 20.5 months

Risultato

Monthly savings: $244 • Break-even point: ~21 months. Refi pays off in <2 years.

4

Low down payment with PMI

Scenario

A $350,000 home, 5% down ($17,500), financed at 7% APR for 30 years. PMI required since LTV > 80%.

Input

Home price
$350,000
Down payment
$17,500 (5%)
Loan amount
$332,500
APR
7%
Term
30 years
PMI rate
0.6%/year

Passaggi del calcolo

  1. P = $332,500
  2. r = 0.07 / 12 = 0.00583
  3. n = 360
  4. M = 332500 × (0.00583 × 1.00583³⁶⁰) / (1.00583³⁶⁰ − 1) ≈ $2,213 / month
  5. PMI: 332500 × 0.006 / 12 = $166 / month
  6. Total PITI (excl. taxes/insurance): $2,213 + $166 = $2,379

Risultato

Monthly: $2,213 P&I + $166 PMI = $2,379. PMI drops off automatically at 78% LTV (after ~5 years of payments) or by appraisal request at 80% LTV.

5

Extra $200/month toward principal

Scenario

Same $320,000 loan, 6.5% APR, 30 years. Adding $200/month to principal.

Input

Loan amount
$320,000
APR
6.5%
Term
30 years
Extra payment
$200/month

Passaggi del calcolo

  1. Base payment: $2,023/month
  2. New payment: $2,023 + $200 = $2,223/month
  3. Time saved: ~7 years (loan paid off in 23 years)
  4. Interest saved: ~$165,000 over the life of the loan

Risultato

Pay $200 extra/month, save ~$165K in interest and 7 years on the loan. Best $200/month you can spend on a mortgage.

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