Finance & Real Estate 7 min read · Published September 3, 2026

Author: Alex Vance (Financial Contributor)

Step-by-step mathematical derivation of fixed-rate mortgage payments and how the front-loaded interest ratio shifts throughout the amortization schedule.

### The Standard Monthly Payment Equation Fixed-rate installment loans use an annuity capitalization formula to calculate a fixed monthly payment $M$: $$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$$ Where: * $P$ = Principal loan amount * $r$ = Periodic monthly interest rate (Annual rate divided by 12) * $n$ = Total number of monthly payment periods (e.g., 360 for a 30-year term) #### Why Early Payments Are "Interest-Heavy" Interest is always assessed on the *remaining principal balance*. On Day 1 of a $400,000 mortgage at 6.5%: * **Month 1 Interest Charge:** $$400,000 \times (0.065 / 12) = **$2,166.67** * **Monthly Payment:** **$2,528.27** * **Principal Reduction in Month 1:** Only **$361.60** (14.3% of your payment!) #### The Accelerator Effect Because Month 1 principal reduction was $361.60, the balance for Month 2 becomes $399,638.40. Next month's interest drops slightly, directing more cash toward principal. When you send an **extra $200 per month** earmarked for principal: * You bypass future compound interest chains for that specific $200 tranche. * On a $400,000 loan, an extra $200/month cuts **4.5 years** off the repayment schedule and eliminates over **$81,000** in lifetime interest payments. Use our interactive **Mortgage Calculator with Amortization Schedule** to simulate extra payments and export full CSV schedules.