Every fixed-rate loan works the same way: each monthly payment is split between interest on the remaining balance and repayment of principal. Early payments are mostly interest; later payments are mostly principal. This is loan amortization — and the fixed monthly payment is calculated by the formula M = P × [r(1+r)^n] / [(1+r)^n − 1], where r is the monthly rate and n is the total number of payments.
The formula
M = P × [r(1+r)^n] / [(1+r)^n − 1]
Where:
- M = monthly payment
- P = loan principal (amount borrowed)
- r = monthly interest rate = annual rate ÷ 12 (as a decimal)
- n = total number of monthly payments = years × 12
Each month's interest charge: Interest = Balance × r
Each month's principal payment: Principal = M − Interest
Remaining balance: Balance = Balance − Principal
Source: Investopedia — Amortization Formula.
Practical examples
Example 1: Auto loan
$25,000 at 7% annual rate for 5 years (60 months):
r = 0.07 / 12 = 0.005833
n = 60
M = 25000 × [0.005833 × (1.005833)^60] / [(1.005833)^60 − 1]
= 25000 × [0.005833 × 1.4176] / [1.4176 − 1]
= 25000 × 0.008270 / 0.4176
= $495.03/month
Total paid: $29,702 · Total interest: $4,702
Example 2: Effect of an extra monthly payment
Same $25,000 loan at 7% for 5 years. Adding $100/month extra:
- Base payment: $495.03
- With extra: $595.03/month
- Months saved: approximately 7
- Interest saved: approximately $420
Example 3: 30-year mortgage comparison
$300,000 at 7% for 30 years vs 15 years:
| Term | Monthly payment | Total interest | Total paid |
|---|---|---|---|
| 30 years | $1,996 | $418,527 | $718,527 |
| 15 years | $2,696 | $185,367 | $485,367 |
The 15-year loan costs $700/month more but saves $233,160 in interest.
Common mistakes
Confusing monthly rate with annual rate. The formula uses the monthly rate (annual ÷ 12). Entering the annual rate directly into a formula expecting a monthly rate gives a wildly incorrect result.
Assuming extra payments reduce future monthly payments. For most standard loans, extra payments reduce the outstanding balance and shorten the loan term — the required monthly payment stays the same. Verify with your lender.
Forgetting that the schedule shows P&I only. The amortization schedule here covers principal and interest. Homeowners also pay property taxes, insurance, and possibly PMI — these are not included here.
Assuming all loans amortize the same way. Adjustable-rate mortgages recalculate the payment periodically. Interest-only loans build no equity during the interest-only period. Balloon loans have a large final payment. This calculator models the standard fixed-rate fully-amortizing loan.
International and regional variations
| Country | Mortgage compounding convention | Notes |
|---|---|---|
| United States | Monthly compounding | Standard for fixed-rate mortgages and consumer loans |
| Canada | Semi-annual compounding (mortgages) | Interest Act requires semi-annual compounding for residential mortgages; effective rate differs from US |
| United Kingdom | Monthly or annual | FCA requires APR disclosure; lenders may compound daily |
| Australia | Monthly or fortnightly | Fortnightly payments reduce effective interest more than halving monthly payments |
| European Union | Varies by country | APRC (Annual Percentage Rate of Charge) required; compounding method set by national law |
Quick reference: monthly payment per $1,000 borrowed
| Annual rate | 5-year loan | 10-year loan | 15-year loan | 30-year loan |
|---|---|---|---|---|
| 4% | $18.42 | $10.12 | $7.40 | $4.77 |
| 5% | $18.87 | $10.61 | $7.91 | $5.37 |
| 6% | $19.33 | $11.10 | $8.44 | $6.00 |
| 7% | $19.80 | $11.61 | $8.99 | $6.65 |
| 8% | $20.28 | $12.13 | $9.56 | $7.34 |
Multiply by your loan amount in thousands to get the approximate monthly payment.