Loan Amortization
An amortizing loan has equal monthly payments where each payment covers accrued interest first, then reduces principal. Early payments are mostly interest; late payments are mostly principal.
Monthly Payment Formula
M = P × [r(1+r)^n] / [(1+r)^n - 1]
P = principal (loan amount)
r = monthly rate = annual rate / 12
n = total payments (months)
$20,000 car loan, 6% annual, 48 months:
r = 0.06/12 = 0.005
M = 20000 × [0.005×1.005⁴⁸] / [1.005⁴⁸-1]
M = 20000 × 0.006419 / 0.2705 = $469.70/monthFirst Few Payments
Month 1:
Interest = 20,000 × 0.005 = $100.00
Principal = 469.70 - 100.00 = $369.70
Balance = 20,000 - 369.70 = $19,630.30
Month 2:
Interest = 19,630.30 × 0.005 = $98.15
Principal = 469.70 - 98.15 = $371.55
Balance = $19,258.75
Month 48 (final):
Almost entirely principal → loan clearedTotal Interest Paid
Total paid = M × n = 469.70 × 48 = $22,545.60
Total interest = 22,545.60 - 20,000 = $2,545.60
(12.7% of loan amount over 4 years)Build amortization schedule: Free Loan Amortization Calculator
Loan Amortization Quick-Reference Table
| Loan ($) | Rate (%/yr) | Term (yr) | Monthly payment | Total interest |
|---|---|---|---|---|
| 100,000 | 4.0 | 15 | $739.69 | $33,144 |
| 100,000 | 4.0 | 30 | $477.42 | $71,870 |
| 200,000 | 6.5 | 30 | $1,264.14 | $255,090 |
| 20,000 | 7.0 | 5 | $396.02 | $3,761 |
| 10,000 | 12.0 | 3 | $332.14 | $1,957 |
How Loan Amortization Works
Monthly payment M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1], where P = principal, r = monthly rate (annual rate / 12), n = total payments. Each payment covers interest (remaining balance × monthly rate) plus principal reduction. Early payments are mostly interest; late payments are mostly principal. This is why extending a 15-year mortgage to 30 years roughly doubles total interest paid despite only cutting the monthly payment by ~35%.
An amortization schedule shows each payment's principal/interest split and the declining balance over time. Extra payments reduce the principal immediately, cutting all future interest charges and shortening the loan term. Making one extra monthly payment per year on a 30-year mortgage can reduce the term by 4–6 years and save tens of thousands in interest. Refinancing makes sense when the interest-rate reduction is large enough to recover closing costs within your planned holding period.
Common Mistakes
- Confusing nominal and effective rates: A 6% annual rate with monthly compounding gives (1 + 0.06/12)¹² − 1 = 6.168% effective annual rate. Mortgage APR includes fees; the nominal rate does not. Always compare APR for true cost comparison between loans.
- Ignoring amortization when comparing loan terms: A 15-year mortgage at 4% costs more per month but dramatically less in total interest than a 30-year at 4%. The correct comparison is total cost of ownership, not monthly payment.
- Not accounting for prepayment penalties: Some mortgages and auto loans charge fees for early payoff. Calculate whether the interest saved by prepaying exceeds the penalty cost before making extra payments.
Frequently Asked Questions
A fixed-rate mortgage locks in the interest rate for the entire term — predictable payments, protected against rising rates but unable to benefit from falling rates. An adjustable-rate mortgage (ARM) has a fixed rate for an initial period (3, 5, or 7 years typically) then resets periodically based on a market index plus a margin. ARMs start lower but carry rate-increase risk. They make sense when you plan to sell or refinance before the adjustment period, or when rates are expected to fall.
Each extra payment directly reduces principal. Lower principal means less interest charged in every subsequent period. A $200,000 mortgage at 5% over 30 years has $186,512 in total interest. Paying $100 extra per month reduces total interest to $143,739 — saving $42,773 and cutting the term from 30 to 25.9 years. The savings are non-linear: extra payments early in the loan save more than the same payments made later.
The break-even rule: divide total closing costs by the monthly savings from the lower rate. If closing costs = $3,000 and monthly savings = $150, break-even is 20 months. If you'll stay in the home longer than 20 months, refinancing makes financial sense. A common heuristic is to refinance if the rate drops by at least 1 percentage point, but the break-even analysis is more precise. Also consider restarting the amortization clock — a lower rate but longer remaining term may increase total interest paid.