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MortgagesLetter A

Amortization

The mathematical scheduling of equal periodic loan payments that systematically reduce both interest and outstanding principal over time.

Overview & Practical Application

Amortization is the systematic reduction of a debt obligation via structured periodic payments over a predetermined timeframe (such as a 15-year or 30-year mortgage, or a 60-month auto loan).

In an amortizing loan, each fixed monthly installment is split into two parts: 1. Interest Portion: Calculated as the outstanding principal balance multiplied by the monthly interest rate. In the early years of a loan, the principal balance is at its peak, so interest consumes the vast majority of each payment. 2. Principal Portion: The remainder of the fixed monthly payment that directly pays down the loan balance.

As the principal balance declines with each consecutive month, the interest charge shrinks, allowing a progressively larger percentage of each monthly payment to be applied directly toward principal reduction.

30-Year Amortization: Principal vs. Interest Over TimeInterest Paid (%/mo)Principal Paid (%/mo)Year 1Year 15 (Crossover)Year 30Early payments are 80%+ interest; principal accelerates in years 16-30.
Visual Infographic: Amortization

Mathematical Formula & Calculation

M = P * [ r(1 + r)^n ] / [ (1 + r)^n - 1 ]

The standard fixed-rate amortization equation to calculate monthly payment M.

Variable Definitions:

  • M=Total monthly payment
  • P=Principal loan amount borrowed
  • r=Periodic monthly interest rate (Annual rate / 12)
  • n=Total number of monthly payments (Years * 12)
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Interactive Financial Calculator

Test real-world numbers and see instant underwriting results.

Monthly Principal & Interest$1,896.20
Total Lifetime Interest Paid$382,633.47
Total Cost of Loan$682,633.47

Real-World Underwriting Example

Scenario: A $300,000 30-year fixed mortgage at 6.00% interest has a monthly principal & interest payment of $1,798.65.

Calculation:
Month 1: Interest = $300,000 * (0.06/12) = $1,500.00. Principal = $298.65.
Month 180 (Year 15): Interest = $1,054.20. Principal = $744.45.
Month 360 (Year 30): Interest = $8.94. Principal = $1,789.71.

Takeaway: Over 30 years, total payments equal $647,514.57 ($300k principal + $347,514.57 total interest paid).

Key Underwriting Takeaways

  • Early mortgage payments are over 80% interest; principal reduction accelerates exponentially in the second half of the term.
  • Making an extra principal-only payment each year dramatically cuts total lifetime interest and shaves years off the loan.
  • Negative amortization occurs if monthly payments do not cover accrued interest, causing the principal balance to grow.
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Rates & InterestAPR

Annual Percentage Rate (APR)

The true annualized cost of borrowing, reflecting the nominal interest rate plus lender origination fees, points, and closing costs.

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Mortgages

Fixed-Rate Mortgage

A home loan where the interest rate and monthly principal and interest payment remain identical for the entire lifespan of the loan.

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