Mortgage Worked Example Pack: 5 Real-World Scenarios

This worked-example pack provides detailed mathematical step-by-step walkthroughs of 5 real-world home loan scenarios.

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Example 1: Standard 30-Year Fixed Mortgage

  • Home Purchase Price: $400,000
  • Down Payment: $80,000 (20%)
  • Loan Principal: $320,000
  • Interest Rate: 6.50% (monthly rate = 0.00541667)
  • Loan Term: 30 Years (360 months)
  • Annual Property Tax: $4,800 ($400 / month)
  • Annual Insurance: $1,200 ($100 / month)

Calculation:

Monthly P&I Payment:

M=320000⋅0.00541667(1.00541667)360(1.00541667)360−1=2022.62M = 320000 \cdot \frac{0.00541667(1.00541667)^{360}}{(1.00541667)^{360} - 1} = 2022.62

Total Monthly PITI = $2,022.62 + $400 + $100 = $2,522.62 / month

Total Lifetime Interest Paid = 360 * $2,022.62 - $320,000 = $408,143.20

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Example 2: 15-Year Accelerated Loan Comparison

  • Loan Principal: $320,000
  • Interest Rate: 5.75% (monthly rate = 0.00479167)
  • Loan Term: 15 Years (180 months)

Calculation:

Monthly P&I Payment:

M=320000⋅0.00479167(1.00479167)180(1.00479167)180−1=2658.07M = 320000 \cdot \frac{0.00479167(1.00479167)^{180}}{(1.00479167)^{180} - 1} = 2658.07
  • Total Interest Paid: 180 * $2,658.07 - $320,000 = $158,452.60
  • Interest Saved vs 30-Year: $408,143.20 - $158,452.60 = $249,690.60

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Example 3: Extra Monthly Principal Prepayment Strategy

  • Current Principal Balance: $320,000
  • Interest Rate: 6.50%
  • Remaining Term: 25 Years (300 months)
  • Standard Monthly P&I: $2,160.66
  • Extra Monthly Prepayment: $200.00 / month

Results:

  • Baseline Total Interest: $328,198.87
  • Accelerated Total Interest: $259,117.01
  • Total Interest Saved: $69,081.86
  • Time Saved Off Loan: 4 Years 6 Months (Payoff in 20.5 years instead of 25 years)

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Example 4: Refinance Break-Even Analysis

  • Current Remaining Principal: $320,000
  • Current Rate & Remaining Term: 6.75% with 25 years remaining (Old Payment = $2,210.92 / mo)
  • New Rate & New Term: 5.50% with 30 years (New Payment = $1,816.92 / mo)
  • Refinance Closing Costs: $4,500

Calculation:

Monthly Savings = $2,210.92 - $1,816.92 = $393.99 / month

Break-Even Period = Ceiling($4,500 / $393.99) = 12 Months

Net Lifetime Benefit = +$4,682.13 (Net of closing costs and term reset).

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Example 5: Low Down Payment PMI Termination Scenario

  • Home Purchase Price: $350,000
  • Down Payment: $17,500 (5% down, LTV = 95%)
  • Base Loan Principal: $332,500
  • Borrower Credit Score: 680
  • Annual PMI Rate: 0.87% (PMI = $241.06 / month)

Automatic Termination Walkthrough:

  • Under the federal Homeowners Protection Act (HPA 1998), PMI automatically terminates when principal balance reaches 78% of original purchase price (78% * $350,000 = $273,000).
  • Through standard monthly payments at 6.5% interest rate, the principal balance drops to $273,000 at Month 102 (Year 8.5).
  • Total PMI Premiums Paid: 102 * $241.06 = $24,588.12.