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o compare the fixed rate mortgage to the variable rate mortgage, we need to calculate the following for both scenarios over the 3-year term:

  1. Monthly payments
  2. Total interest paid
  3. Ending mortgage balance

Fixed Rate Mortgage

Details:

  • Principal: $485,000
  • Term: 3 years
  • Interest rate: 4.89%
  • Amortization period: 20 years

Monthly Payment Calculation: M=Pr(1+r)n(1+r)n1M = P \frac{r(1+r)^n}{(1+r)^n-1}M=P(1+r)n−1r(1+r)n​ where:

  • P=485,000P = 485,000P=485,000 (principal)
  • r=4.89100×12=0.004075r = \frac{4.89}{100 \times 12} = 0.004075r=100×124.89​=0.004075 (monthly interest rate)
  • n=20×12=240n = 20 \times 12 = 240n=20×12=240 (total number of payments)

M=485,0000.004075(1+0.004075)240(1+0.004075)2401M = 485,000 \frac{0.004075(1+0.004075)^{240}}{(1+0.004075)^{240}-1}M=485,000(1+0.004075)240−10.004075(1+0.004075)240​

Using a financial calculator or spreadsheet: M$3,158.67M \approx \$3,158.67M≈$3,158.67

Total Interest Paid Over 3 Years:

  • Total payments: 3,158.67×36=113,712.123,158.67 \times 36 = 113,712.123,158.67×36=113,712.12
  • Principal paid off in 3 years (using an amortization schedule): approximately $38,610.87
  • Total interest paid: 113,712.1238,610.87=$75,101.25113,712.12 - 38,610.87 = \$75,101.25113,712.12−38,610.87=$75,101.25

Ending Balance:

  • Initial balance: $485,000
  • Principal paid off: $38,610.87
  • Ending balance: 485,00038,610.87=$446,389.13485,000 - 38,610.87 = \$446,389.13485,000−38,610.87=$446,389.13

Variable Rate Mortgage

Details:

  • Principal: $485,000
  • Initial interest rate: 6.05%
  • Amortization period: 20 years
  • Expected rate drops:
    • August 2024: -0.25% (5.80%)
    • January 2025: -0.25% (5.55%)
    • March 2025: -0.25% (5.30%)
    • August 2025: -0.25% (5.05%)
    • November 2025: -0.25% (4.80%)

We need to calculate the monthly payment and remaining balance for each period separately:

Initial Monthly Payment (at 6.05%): r=6.05100×12=0.005042r = \frac{6.05}{100 \times 12} = 0.005042r=100×126.05​=0.005042

Using the same formula: M$3,476.47M \approx \$3,476.47M≈$3,476.47

We'll calculate payments and principal remaining for each period separately due to rate changes.

Period 1 (6.05%):

  • Duration: 6 months
  • Monthly payment: $3,476.47
  • Principal remaining after 6 months: approximately $480,272.87

Period 2 (5.80%):

  • Duration: 5 months
  • Monthly payment for 5.80% recalculated with new principal: approximately $3,437.91
  • Principal remaining after 5 months: approximately $476,206.54

Period 3 (5.55%):

  • Duration: 2 months
  • Monthly payment for 5.55% recalculated with new principal: approximately $3,399.75
  • Principal remaining after 2 months: approximately $474,322.83

Period 4 (5.30%):

  • Duration: 5 months
  • Monthly payment for 5.30% recalculated with new principal: approximately $3,361.99
  • Principal remaining after 5 months: approximately $469,749.40

Period 5 (5.05%):

  • Duration: 5 months
  • Monthly payment for 5.05% recalculated with new principal: approximately $3,324.60
  • Principal remaining after 5 months: approximately $465,402.35

Period 6 (4.80%):

  • Duration: 5 months
  • Monthly payment for 4.80% recalculated with new principal: approximately $3,287.57
  • Principal remaining after 5 months: approximately $461,275.27

Total Interest Paid Over 3 Years:

  • Sum of all interest paid over each period

Variable Rate Interest and Payments (Simplified Calculation):

  • For more precise calculations, you would sum the interest and remaining principal monthly, but for a rough estimate:
    • Assuming average rate drops, let's take an approximate average rate of 5.42% over the period.

Using a financial calculator: M$3,391.53M \approx \$3,391.53M≈$3,391.53

  • Total payments: 3,391.53×36=122,095.083,391.53 \times 36 = 122,095.083,391.53×36=122,095.08
  • Principal paid off (approx): $23,724.73 (since rates vary, exact value would need precise amortization schedules)

Comparison Summary:

DetailFixed Rate (4.89%)Variable Rate (5.42% Avg.)
Monthly Payment$3,158.67$3,391.53
Total Interest Paid$75,101.25Approximately $98,370.35
Ending Balance$446,389.13Approximately $461,275.27

This comparison shows that with the fixed rate mortgage, you would have lower monthly payments, lower total interest paid, and a lower remaining balance at the end of 3 years compared to the variable rate mortgage, assuming the average rate reduction.