Understanding Loan Payments: How Monthly Payments Are Calculated
2026-02-12
How Are Loan Payments Calculated?
When you borrow money, your monthly payment depends on three factors:
- Principal (P): The amount you borrow
- Interest Rate (r): The annual interest rate, divided by 12 for monthly
- Loan Term (n): The number of monthly payments (years × 12)
The Amortization Formula
M = P × [r(1+r)^n] / [(1+r)^n - 1]Where:
- M = monthly payment
- P = loan principal
- r = monthly interest rate (annual rate ÷ 12 ÷ 100)
- n = total number of payments
A Practical Example
Let's say you take out a $250,000 mortgage at 6.5% annual interest for 30 years:
- P = $250,000
- r = 6.5% ÷ 12 ÷ 100 = 0.00542
- n = 30 × 12 = 360 payments
Over the life of the loan:
- Total Paid: $568,861
- Total Interest: $318,861
How to Reduce Your Total Interest
- Make extra payments: Even $100/month extra can save thousands
- Choose a shorter term: A 15-year mortgage has higher payments but much less total interest
- Get a lower rate: Improving your credit score can qualify you for better rates
- Refinance: If rates drop, refinancing can reduce your payment
15-Year vs 30-Year Mortgage
For a $250,000 loan at 6.5%:
- 30-year: $1,580/month, $318,861 total interest
- 15-year: $2,177/month, $141,868 total interest
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