How to Calculate a Loan Amortization Schedule Step-by-Step
When you take out a fixed-rate loan—whether for a mortgage, personal financing, or an auto purchase—your monthly payment stays constant, but the underlying split between principal and interest shifts every single month. This structured payment breakdown is called an amortization schedule.
1. The Monthly Amortization Payment Formula
The standard monthly installment ($PMT$) is calculated using the annuity formula:
- P = Principal loan amount
- r = Monthly interest rate (Annual Rate ÷ 12 ÷ 100)
- n = Total number of monthly payments (Loan term in years × 12)
2. Step-by-Step Calculation Breakdown
Let's calculate a $10,000 loan at 5.0% annual interest over 36 months (3 years):
- Monthly Rate ($r$): 0.05 ÷ 12 =
0.0041667 - Total Months ($n$): 3 × 12 =
36 months - Monthly Payment ($PMT$): Applying the formula yields
$299.71 per month.
3. Month-by-Month Interest vs Principal Split
In month 1, interest is charged on the full $10,000 starting balance:
- Month 1 Interest: $10,000 × 0.0041667 = $41.67
- Month 1 Principal: $299.71 - $41.67 = $258.04
- New Balance: $10,000 - $258.04 = $9,741.96
In month 2, interest is calculated on $9,741.96 (which equals $40.59), allowing $259.12 to go toward principal. By month 36, interest drops to under $1.25, and the balance reaches exactly $0.00.
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