An amortizing loan is repaid in equal monthly payments, and each payment is split into interest on what you still owe and the part that reduces the loan. Early on, nearly all of it is interest; the split turns around slowly. For a loan of 200,000 at 6% a year over 30 years the payment is 1,199.10, and the very first payment is 1,000.00 interest and only 199.10 repayment. Over 360 payments you pay 231,677.04 in interest, which is more than the loan itself. This article gives the formula, shows the schedule at several points, explains why paying a little extra early is so powerful, and shows how to reproduce it all with a calculator. Every figure here was calculated twice, once with the loan calculator's own logic and once with an independent script.
The payment formula
For a loan of P repaid in n monthly payments at a monthly rate r, the equal payment is:
M = P × r × (1 + r)^n / ((1 + r)^n − 1)The monthly rate is the yearly rate divided by 12. For 200,000 at 6% over 30 years: r = 0.06 ÷ 12 = 0.005 and n = 360. The growth factor (1.005)^360 is 6.0226, so
M = 200,000 × 0.005 × 6.0226 / (6.0226 − 1) = 1,000 × 1.19910 = 1,199.10More exactly, the unrounded value is 1,199.1010…, which rounds to 1,199.10. If the rate is 0%, the formula does not work, and the payment is simply P ÷ n.
How a payment is split
Each month the same three steps repeat:
- Interest = balance ×
r. In month 1 that is 200,000 × 0.005 = 1,000.00. - Principal repaid = payment − interest = 1,199.10 − 1,000.00 = 199.10.
- New balance = old balance − principal repaid = 199,800.90.
Next month the interest is charged on 199,800.90, so it is 999.00 and the principal part is 200.10, and so on. Nothing changes except that the balance falls a little, which makes the interest a little smaller, which leaves a little more for principal.
The schedule at several points
| Payment no. | Payment | Interest | Principal | Balance after |
|---|---|---|---|---|
| 1 | 1,199.10 | 1,000.00 | 199.10 | 199,800.90 |
| 2 | 1,199.10 | 999.00 | 200.10 | 199,600.80 |
| 3 | 1,199.10 | 998.00 | 201.10 | 199,399.70 |
| 12 | 1,199.10 | 988.77 | 210.33 | 197,543.99 |
| 60 | 1,199.10 | 931.88 | 267.22 | 186,108.80 |
| 120 | 1,199.10 | 838.66 | 360.44 | 167,371.60 |
| 180 | 1,199.10 | 712.92 | 486.18 | 142,097.98 |
| 223 | 1,199.10 | 596.63 | 602.47 | 118,723.08 |
| 240 | 1,199.10 | 543.32 | 655.78 | 108,007.66 |
| 300 | 1,199.10 | 314.55 | 884.55 | 62,024.90 |
| 360 | 1,200.14 | 5.97 | 1,194.17 | 0.00 |
Payment 223, in the 19th year, is the first one where principal is larger than interest. Before it, more than half of every payment goes to interest.
Why the early years are so interest-heavy
Interest is charged on what you owe, and at the start you owe all of it. The numbers for this loan:
- In the first 12 payments you pay 11,933.19 in interest and reduce the loan by only 2,456.01.
- After 5 years the balance is still 186,108.80, so you have repaid 13,891.20 of the 200,000.
- After 10 years you have paid 1,199.10 × 120 = 143,892.00 in total, of which 111,263.60 is interest and only 32,628.40 is principal, so the balance is still 167,371.60.
This is why selling or refinancing a loan in the first years leaves you owing almost as much as you borrowed.
Term changes the cost sharply
For the same 200,000 at 6%:
| Term | Monthly payment | Total interest |
|---|---|---|
| 10 years | 2,220.41 | 66,449.21 |
| 15 years | 1,687.71 | 103,788.82 |
| 20 years | 1,432.86 | 143,887.30 |
| 30 years | 1,199.10 | 231,677.04 |
Going from 30 to 15 years raises the payment by 488.61 a month and cuts the interest by 127,888.22. A longer term lowers the monthly burden and raises the total cost, and both facts matter.
Total cost and the last payment
Total paid for the 30-year loan is 431,677.04: the 200,000 borrowed plus 231,677.04 of interest, about 2.16 times the amount. The final payment, 1,200.14, is 1.04 more than the others. The regular payment is rounded to the cent, so after 359 payments the balance would not land on exactly zero. The last payment is therefore whatever clears the balance. A bank may round in a different way, for example always down, so its own schedule can differ by a few cents.
What an extra payment does
An extra amount paid every month goes straight to principal, which lowers the balance on which next month's interest is charged. For 200,000 at 6% over 30 years:
| Extra per month | Payments needed | Time | Total interest | Interest saved | Last payment |
|---|---|---|---|---|---|
| 0 | 360 | 30 years | 231,677.04 | 0 | 1,200.14 |
| 100 | 295 | 24 years 7 months | 182,538.19 | 49,138.85 | 602.79 |
| 200 | 252 | 21 years | 151,876.18 | 79,800.86 | 702.08 |
| 500 | 179 | 14 years 11 months | 102,534.49 | 129,142.55 | 94.69 |
Adding 200 a month, about 17% on top of the 1,199.10 payment, shortens the loan by 9 years and saves 79,800.86. The earlier the extra money is paid, the more it saves, because it removes principal that would have attracted interest for years. Before relying on it, ask your lender three questions: is there a fee for early repayment, does the extra money go to principal rather than to next month's payment, and is the interest calculated monthly like this or daily.
Equal payments or equal principal
Some lenders use a second method, in which every payment repays the same slice of the loan plus interest on what is left. The payments therefore fall over time. Take 12,000 at 12% a year over 12 months. With equal principal the first payment is 1,120.00, the last is 1,010.00 and the interest totals 780.00. With equal payments every payment is about 1,066.19 and the interest totals 794.23. The falling schedule costs less in interest but asks for more cash at the start. Which suits you depends on your budget.
Reproducing it with the calculator
- Open the loan calculator. Enter the Loan amount (200000), the Interest rate per year (%) (6) and the Loan term, with "Term in" set to Years (30) or Months (360).
- Choose Repayment: "Equal monthly payments" or "Equal principal, falling payments".
- Optionally enter Extra payment each month, and a Loan start date to see calendar dates in the schedule.
- Read Monthly payment, Total interest, Total paid, First payment, Last payment and Paid off in. With an extra amount, a sentence says how much sooner the loan ends and how much interest you save.
- Scroll the schedule, or press "Copy CSV" or "Download CSV" to take it to a spreadsheet; the CSV and JSON converter can turn that file into JSON, and the article on converting CSV to JSON covers the traps.
Amounts and rates can be typed as 1,234.56 or 1.234,56, and the tool shows how it read them. It handles loans up to 100 billion, terms up to 600 months and rates up to 100% a year. The sums are done in whole cents inside your browser, with nothing uploaded. To check the arithmetic of a percentage on its own, use the percentage calculator.
What this model leaves out
It is a fixed rate, monthly payments at the end of each month, fully repaid loan. It does not include variable or promotional rates, interest-only periods, balloon payments, fees, insurance, taxes or daily interest. The rate used is the nominal yearly rate divided by 12, not the APR, which includes fees and is calculated differently. Treat the result as an estimate for comparing options, not as financial advice or an offer.
A short checklist
Convert the yearly rate to a monthly one, divide by 12. Expect the first payments to be mostly interest. Compare terms by total interest as well as the monthly payment. Test an extra payment of different sizes, and check with the lender about fees and where the money is applied. Remember that a real quote will include costs this model does not.