Reference chart
How a Loan Amortizes
By &Pixels, the studio that builds MyCalculator.to. Figures use a $300,000 loan at 7 percent over 30 years. The shape holds at any rate; only the numbers move.
Where each payment actually goes, year by year, and why it takes until year 21 to repay half the principal on a 30 year loan.
What is loan amortization?
Amortization is the schedule by which a fixed payment is split between interest and principal. The payment stays the same every month, but the split does not: interest is charged on the outstanding balance, so as the balance falls the interest portion shrinks and the principal portion grows.
The consequence is severe at the start. On a $300,000 loan at 7 percent, the first payment of $1,996 puts about $1,750 toward interest and $246 toward the balance. It takes until roughly year 21 to have repaid half the principal, which is not what "halfway through a 30 year mortgage" sounds like.
Where the money goes, by year
| Year | To principal | To interest | Balance | Repaid |
|---|---|---|---|---|
| 1 | $3,059 | $20,892 | $296,941 | 1.0% |
| 3 | $3,502 | $20,449 | $290,163 | 3.3% |
| 5 | $4,029 | $19,922 | $282,375 | 5.9% |
| 10 | $5,700 | $18,251 | $255,713 | 14.8% |
| 15 | $8,065 | $15,886 | $217,984 | 27.3% |
| 20 | $11,411 | $12,540 | $164,596 | 45.1% |
| 21 | $12,237 | $11,714 | $152,359 | 49.2% |
| 25 | $16,146 | $7,805 | $92,857 | 69.0% |
| 28 | $19,890 | $4,061 | $36,146 | 88.0% |
| 30 | $23,058 | $893 | $0 | 100% |
Year 21 is the row worth sitting with. Two thirds of the way through the term, and only half the loan is repaid. The last nine years do as much work on the balance as the first twenty-one.
The calculators behind this
What an extra payment does
Extra money applied to principal skips the interest step entirely, which is why it is worth so much more than its face value. Same loan, an extra amount every month from the start.
| Extra per month | Paid off in | Interest saved |
|---|---|---|
| $0 | 30 years | baseline |
| $100 | 26 yr 4 mo | about $66,000 |
| $200 | 23 yr 9 mo | about $111,000 |
| $300 | 21 yr 9 mo | about $145,000 |
| $500 | 18 yr 10 mo | about $193,000 |
How the split is calculated
- Work out the monthly rate. Annual rate divided by 12. A 7 percent loan charges 0.5833 percent a month.
- Multiply it by the current balance. That is the interest portion of this month’s payment, and it changes every month.
- Subtract that from the payment. Whatever is left reduces the principal. Early on, very little is left.
- Take the new balance into next month. A smaller balance means less interest, so slightly more goes to principal. That is the whole mechanism.
- Apply any extra payment to principal. It skips the interest step entirely, which is why an extra payment early is worth far more than a late one.
For your own loan rather than this example, the amortization calculator prints every payment with its split and running balance, and the loan amortization schedule exports the whole thing if you would rather work in a spreadsheet.
These figures are arithmetic, not advice. What a loan should cost you and whether to take one are questions for someone who knows your circumstances.
Formula & Methodology
Formula
M = P[r(1+r)^n] / [(1+r)^n - 1]M = the fixed monthly payment
P = principal, the amount borrowed
r = monthly interest rate, the annual rate divided by 12
n = total number of payments, months rather than years
Worked Example
$300,000 at 7 percent over 30 years
Did you know? The word amortize comes from the Latin for 'to kill off'. It describes killing the debt gradually, and the schedule is literally a record of how slowly that happens at the start.
Sources
- Consumer Financial Protection Bureau, mortgage and loan disclosure guidance
- Standard amortisation formula as used in Regulation Z disclosures