The quick answer: ask for three numbers, not one
A lender quotes a monthly payment. That tells you what leaves your account each month and nothing about what the loan costs. Look for three numbers: the payment, the total of all payments, and the total interest, which is the total paid minus the amount borrowed. The loan calculator gives all three from an amount, a yearly interest rate and a term, plus a payment schedule you can download.
- Enter the amount borrowed, the yearly interest rate and the term.
- Read the monthly payment, the total interest and the total of all payments.
- Open Extra payments and enter an extra amount to see the interest saved, or press Download CSV for the schedule.
Here is a small example you can check by hand. It uses 6% a year, an example rate and not one you will get. Borrow 10,000 for 3 years and the payment is 304.22 a month. You pay 10,951.88 in total, and 951.88 of that is interest.
How the payment is worked out
In the usual textbook model, and in the loan calculator, each month the lender charges interest on what you still owe, at one twelfth of the yearly rate. Your payment covers that interest first, and whatever is left reduces the balance. A standard loan uses one fixed payment, chosen so the balance reaches exactly zero after the last one:
- payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
- P is the amount borrowed, r is the monthly rate (the yearly rate ÷ 12 ÷ 100) and n is the number of monthly payments.
For 10,000 at 6% over 36 months, r = 6 ÷ 12 ÷ 100 = 0.005 and n = 36. Then (1.005)^36 is about 1.19668, so the payment is 10,000 × 0.005 × 1.19668 ÷ 0.19668 = 304.22. At 0% the payment is just the loan divided by the number of payments.
To get the total interest, multiply the payment by the number of payments and subtract the loan. Here 304.22 × 36 = 10,951.92, a few cents above the true 10,951.88. The schedule explains the gap: every payment is rounded to the cent, so the last one is 304.18, just enough to clear what is left.
Why early payments are mostly interest, and how to read a schedule
Interest is charged on the balance, and the balance is largest at the start. A payment schedule shows the split for every month. This is the example loan, with each month's interest rounded to the cent:
| Month | Payment | Interest | Principal | Balance after |
|---|---|---|---|---|
| 1 | 304.22 | 50.00 | 254.22 | 9,745.78 |
| 2 | 304.22 | 48.73 | 255.49 | 9,490.29 |
| 3 | 304.22 | 47.45 | 256.77 | 9,233.52 |
| 12 | 304.22 | 35.66 | 268.56 | 6,864.06 |
| 24 | 304.22 | 19.10 | 285.12 | 3,534.68 |
| 36 | 304.18 | 1.51 | 302.67 | 0.00 |
You can rebuild any row. Month 2 interest is the previous balance times the monthly rate: 9,745.78 × 0.005 = 48.73. Principal is the payment minus the interest: 304.22 − 48.73 = 255.49. The new balance is 9,745.78 − 255.49 = 9,490.29. Interest shrinks a little every month and principal grows by the same amount.
On a longer loan the early split is more lopsided. For 250,000 at an example 6.5% over 30 years, the payment is 1,580.17 and month 1 interest is 250,000 × 6.5 ÷ 1,200 = 1,354.17 (rounded to the cent). Only 226.00 reduces the loan, so about 86% of the first payment is interest.
Term versus payment: the trade in numbers
A longer term lowers the payment and raises the total interest, because the balance stays high for longer. Here is one loan of 250,000 at an example rate of 6.5% (an example, not a rate you will get) over five terms:
| Term | Monthly payment | Total interest | Total paid |
|---|---|---|---|
| 10 years | 2,838.70 | 90,644 | 340,644 |
| 15 years | 2,177.77 | 141,998 | 391,998 |
| 20 years | 1,863.93 | 197,345 | 447,345 |
| 25 years | 1,688.02 | 256,405 | 506,405 |
| 30 years | 1,580.17 | 318,862 | 568,862 |
Going from 30 years to 15 raises the payment by 597.60 a month and cuts the interest by roughly 176,900. In the 30 year row the interest is more than the 250,000 borrowed. The table shows the trade, not which row is right for anyone.
Small rate changes matter too. On the 10,000 example over 36 months, moving from 6% to 7% is 1 percentage point, or a 16.67% relative rise in the rate (see percentage calculations explained for the difference). The payment rises only from 304.22 to 308.77, about 1.5%. The total interest rises from 951.88 to 1,115.76, about 17.2%. The payment hides most of the change.
What extra payments do
An extra payment goes straight to the balance, so every later month's interest is charged on a smaller number. On the 250,000 loan at the example 6.5%, adding 200 a month ends the loan after 265 payments (22 years and 1 month) instead of 360. The interest falls from about 318,862 to about 221,243, a saving of roughly 97,600 and 7 years 11 months.
Put that against what you paid in. The extra 200 went in for 264 months, which is 52,800, so about 52,800 of extra payments removed roughly 97,600 of interest. Small regular amounts matter more than they look because they start working in the first month.
Check two things with your lender before relying on this. Some loans charge a fee for repaying early, and some need you to say that the extra amount should go to principal rather than to the next payment. The loan calculator shows the saving for your own numbers under Extra payments.
Interest rate, flat rate and APR
Ask what the rate applies to. If 5% a year is charged on the original amount for every year of the term, that is simple interest: 10,000 × 0.05 × 3 = 1,500, which the simple interest calculator works out. If 5% a year is charged on the balance that remains, one twelfth of it each month as in the loan calculator, the same 10,000 over 36 months has a payment of 299.71 and total interest of 789.54. The words around a rate matter.
Many lenders also quote an APR, which rolls some fees into a yearly rate. The calculator uses the plain interest rate and leaves out fees, insurance, taxes, rates that change, other compounding rules and weekly plans.
The payment formula is compound interest run in reverse: the balance grows by r each month, and your payment pulls it back down. The compound interest calculator shows the growing side.
Mortgages: the same formula plus costs you enter
A mortgage payment uses the same formula for principal and interest. The difference is the extras, such as property tax and home insurance, which are often collected with the payment. Amounts and rules differ widely by country, region and lender, so the mortgage calculator has no built-in figures. It uses the amounts you type in.
For a 300,000 home with 20% down (a loan of 240,000) at 6.5% over 30 years, principal and interest is 1,516.96. Add example figures of 3,600 a year for property tax (300 a month) and 1,200 a year for insurance (100 a month) and the total is 1,916.96. About a fifth of that goes to things other than the loan.
Mortgage CalculatorEnter a price, a down payment, a rate and a term, add your own tax and insurance, and compare terms side by side.Open it