Loan amortization: equal-payment vs equal-principal
Loans typically use equal-payment (fixed monthly payment) or equal-principal (fixed principal portion) repayment. This article walks through the math and behavior.
Equal-payment: same amount each month
The most common mortgage style. The monthly payment (principal + interest combined) stays constant.
Monthly payment M:
M = P × r × (1 + r)^n / ((1 + r)^n - 1)- P — principal (borrowed amount)
- r — monthly interest rate (annual / 12)
- n — number of payments (months)
Example: $300,000, 1.0% annual, 35 years (420 payments):
- r = 0.01 / 12 ≒ 0.000833
- M = 300,000 × 0.000833 × (1.000833)^420 / ((1.000833)^420 − 1) ≒ $847
Equal-principal: principal portion is constant
The principal repaid each month is fixed; interest decreases as the balance shrinks.
- Month 1 principal — P / n
- Month 1 interest — P × r
- Month 1 total — P / n + P × r
Payments start high and shrink over time.
Comparing the two
| Property | Equal-payment | Equal-principal |
|---|---|---|
| Monthly payment | Constant | Starts high, decreases |
| Total interest | Higher | Lower |
| Early burden | Lighter | Heavier |
| Planning | Simple (fixed) | Variable |
For $300,000 / 1.0% / 35 years:
- Equal-payment — total ~$355,700 (interest ~$55,700)
- Equal-principal — total ~$352,700 (interest ~$52,700)
Difference is about $3,000. Equal-principal saves interest but costs more upfront.
Principal vs interest mix shifts
In equal-payment loans, the split changes over time:
- Early on — most of each payment is interest.
- Later — most is principal.
For $300,000 / 1.0% / 35 years:
| # | Payment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | 847 | 250 | 597 | 299,403 |
| 120 | 847 | 198 | 649 | 237,910 |
| 240 | 847 | 135 | 712 | 162,470 |
| 420 | 847 | ~0 | 846 | 0 |
The “interest is eating my payment” feeling is real early in the loan.
Prepayment
Two prepayment styles:
Term reduction
Shorten the loan duration. Maximum interest savings.
Example: $300,000 / 1.0% / 35 years, $20,000 prepayment in year 10:
- Term reduced — about 2 years 6 months
- Interest saved — about $8,000
Payment reduction
Lower the monthly payment, keep the term. Less interest savings than term reduction but immediate budget relief.
“Save interest” → term reduction. “Lower monthly cost” → payment reduction.
Fixed vs variable rate
Fixed rate
Rate locked for the full term.
- Pro — predictable payments, easy budgeting.
- Con — usually higher rate than variable.
Variable rate
Rate adjusts (typically every 6 months).
- Pro — lower rate when market rates are low.
- Con — exposure if rates rise.
Common consumer protections (Japan’s “5-year rule” and “125% rule”):
- Payment doesn’t change for 5 years.
- At reset, payment can rise at most 1.25× the prior payment.
But unpaid interest can accumulate behind the scenes.
How much can you borrow?
Rule of thumb on debt-to-income:
- Debt-service ratio — annual payments / annual income.
- Generally 25–30% maximum.
$60,000/year income → $15,000–$18,000/year in payments → $1,250–$1,500/month.
$300,000 / 1.0% / 35 years is $847/month — comfortable for that income.
Bonus payments (Japan-style)
Some Japanese loans split the principal: $X each month + $Y at bonus seasons (June, December).
- Bonus principal is amortized as semi-annual payments.
- Each stream uses its own formula.
If bonuses shrink, repayment gets tight. “Zero-bonus” structures have become more common.
Pitfalls when computing
- Rate units — convert annual to monthly (annual / 12).
- Equal-payment formula — derived from compound interest, not “principal / months + flat interest”.
- Fees and insurance — included in real total cost.
- Credit life insurance — sometimes baked into the rate, sometimes separate.
“Just the rate” or “principal + interest” understates real cost.
Summary
- Equal-payment is constant; equal-principal front-loads cost.
- Equal-payment is more complex but easier to plan.
- Term-reduction prepayment saves the most interest.
- Variable rates carry adjustment-cap rules (read the fine print).
For monthly-payment scenarios from principal, rate, and term, the loan calculator on this site handles both styles.