How to Calculate Loan Payments: The Formula Explained
Understanding how loan payments are calculated helps you compare offers, plan budgets, and avoid overpaying. Here's the complete guide.
The Loan Payment Formula
M = P × [r(1+r)^n] / [(1+r)^n - 1]
Where:
- M = monthly payment
- P = principal (loan amount)
- r = monthly interest rate (annual rate ÷ 12)
- n = total number of payments (years × 12)
Worked Example
Loan: $20,000 car loan at 6% annual interest for 5 years.
- P = 20,000
- r = 6% ÷ 12 = 0.5% = 0.005
- n = 5 × 12 = 60 payments
M = 20,000 × [0.005 × (1.005)^60] / [(1.005)^60 - 1]
M = 20,000 × [0.005 × 1.3489] / [1.3489 - 1]
M = 20,000 × 0.006745 / 0.3489
M = 20,000 × 0.01933
M ≈ $386.66 per month
Over 60 months: $386.66 × 60 = $23,199.60 total. You pay $3,199.60 in interest.
How Interest Rate Affects Payments
| Loan | Rate | Monthly | Total Interest | |------|------|---------|----------------| | $20,000, 5yr | 4% | $368.33 | $2,099.80 | | $20,000, 5yr | 6% | $386.66 | $3,199.60 | | $20,000, 5yr | 8% | $405.53 | $4,331.80 | | $20,000, 5yr | 10% | $424.94 | $5,496.40 |
A 4% difference in rate adds over $3,000 in interest on a modest car loan.
How Loan Term Affects Payments
| Loan | Term | Monthly | Total Interest | |------|------|---------|----------------| | $20,000, 6% | 3 years | $608.44 | $1,903.84 | | $20,000, 6% | 5 years | $386.66 | $3,199.60 | | $20,000, 6% | 7 years | $292.57 | $4,575.88 |
Longer term = lower monthly payments but significantly more total interest.
The Amortization Schedule
Each monthly payment splits into interest and principal. In the early months, most of your payment is interest. Over time, more goes to principal — this is called amortization.
Month 1 of $20,000 loan at 6%:
- Interest: $20,000 × 0.005 = $100.00
- Principal: $386.66 - $100.00 = $286.66
- Remaining balance: $19,713.34
Month 60:
- Interest: ~$1.93
- Principal: ~$384.73
- Remaining balance: $0
Extra Payments Save a Lot
Adding even $50/month extra to your loan payment reduces both the term and total interest significantly. The extra payment goes entirely to principal, reducing future interest charges.
Use our Loan Calculator to see your exact payment schedule, total interest, and the impact of extra payments.