Mortgage Amortization Guide

Mortgage Amortization: The Mathematical Framework

Mortgage amortization is the process of paying off a debt over time through regular payments. A portion of each payment is for interest while the remaining amount is applied towards the principal balance.

The Amortization Formula

The standard fixed-rate mortgage formula is derived from the "Present Value of an Annuity" equation:

Where M is monthly payment, P is principal, i is monthly interest, and n is number of months.

The Effect of Interest Compounding

Mortgages typically use monthly compounding. This means interest is calculated based on the remaining balance at the end of each month. In the early years, the majority of your payment goes toward interest because the principal balance is at its peak.

LTV and Down Payment Strategies

The **Loan-to-Value (LTV)** ratio is a critical factor for lenders. A 20% down payment (80% LTV) is the industry benchmark. Falling below this often triggers the requirement for Private Mortgage Insurance (PMI) in many jurisdictions, which adds significant cost without reducing your principal.

Global Variations in Lending

• USA: Dominated by 30-year fixed-rate loans with federal backing (FHA/VA).
• Europe: Often utilizes shorter fixed terms (5-10 years) followed by floating rates.
• Asia: High-growth markets often see a mix of repo-linked floating rates.