How a loan payment splits.
Each fixed payment splits between interest (on the outstanding balance) and principal (the rest). Because the balance falls each period, the interest portion shrinks and the principal portion grows. The math is unsurprising; the curve is steep.
The two equations
For a fixed-rate amortising loan, two equations govern every period:
interestk = balancek-1 · r
principalk = PMT − interestk
balancek = balancek-1 − principalk
where k is the period index (1, 2, 3, ...), r is the periodic interest rate, and PMT is the constant payment. Iterate from k=1 with balance0 = principal; the schedule terminates when balancek ≤ 0.
Why the principal portion grows geometrically
From the equations above, you can derive that the principal portion of each payment grows by a factor of (1 + r) each period:
principalk+1 = principalk · (1 + r)
So the principal portion of the last payment of a 25-year monthly loan at 6% is (1.005)299 ≈ 4.46× the principal portion of the first payment. The interest portion mirrors this exactly — declining at the same compound rate.
The 50/50 cross-over
The month at which principal paid first exceeds interest paid is the “50/50 point”. For a 30-year monthly mortgage at 6%, this happens around month 222 (year 18.5). For a 25-year at 6%, around month 175 (year 14.5). For a 25-year at 4%, around month 145 (year 12).
The cross-over moves earlier when the rate is lower (more of each payment is principal from the start) and earlier when the term is shorter (less time for interest to accumulate at the front).
Reference: $200k loan at 6%, 25-year monthly schedule
| Year | Year-end balance | Year's principal | Year's interest | Interest % |
|---|---|---|---|---|
| 1 | $196,200 | $3,800 | $11,800 | 76% |
| 5 | $176,300 | $4,820 | $10,780 | 69% |
| 10 | $144,000 | $6,495 | $9,105 | 58% |
| 15 | $100,500 | $8,750 | $6,850 | 44% |
| 20 | $42,100 | $11,790 | $3,810 | 24% |
| 25 | $0 | $15,160 | $440 | 3% |
Year 1: $11,800 of every $15,600 paid is interest. Year 25: just $440. The arithmetic is the same in every period; only the input (the outstanding balance) changes.
Why this matters for selling, refinancing, and overpaying
- Selling early. If you sell at year 5 of a 25-year loan, you have built only ~$23,500 of equity from amortisation alone. The bulk of any equity gain came from price appreciation and your original deposit, not from paying down the loan.
- Overpayments are most powerful early. An extra dollar of principal in month 1 saves the interest that dollar would have accrued for 299 more months. The same dollar in month 280 saves only 20 months of interest. The leverage is real and decays.
- Refinancing trade-offs. Restarting a 25-year clock when refinancing a partway-amortised loan is rarely the right answer, even at a substantially lower rate. The refinance decision page walks through the math.