The Amortization Formula Behind Loan Comparison
The calculator uses the standard amortization formula to determine payments for both loans:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
Where P is the principal, i is the monthly interest rate (annual rate / 12), and n is the total number of monthly payments. It then simulates both loans month-by-month, tracking cumulative interest and total payments to determine the true financial difference after including refinancing costs.
Worked Example: $95,000 Mortgage Refinance
Consider a homeowner with $95,000 remaining at 6.5%, paying $632/mo with 300 payments left, exploring a new 30-year loan at 5% with $3,000 in closing costs.
| Metric | Current Loan | New Loan |
|---|---|---|
| Monthly Payment | $632.00 | $509.98 |
| Total Interest | $101,917.81 | $88,593.00 |
| Total Cost | $196,917.81 | $186,593.00 |
| Monthly Savings | -- | $122.02 |
| Break-Even | -- | 24.6 months |
| Net Savings | -- | $10,324.81 |
The new payment is calculated as: $95,000 x [0.004167 x (1.004167)^360] / [(1.004167)^360 - 1] = $509.98/mo. Break-even = $3,000 / $122.02 = 24.6 months. Total savings = $196,917.81 - $186,593.00 = $10,324.81.
When Refinancing Costs More Than It Saves
Not every rate drop justifies refinancing. Extending a near-finished loan to a new 30-year term can wipe out interest savings. For instance, dropping from 6.5% to 6.0% on the same $95,000 balance saves only $62.43/mo, but stretching to 360 payments costs $11,128 more overall. Always check total savings, not just the monthly payment reduction.