How the result is calculated
The calculator page states the payment formula; this guide follows what that formula does across a whole term. Early on, most of the payment is interest because the balance is high; towards the end almost all of it is principal. Laid out payment by payment, that split is the amortisation schedule, and it is what this calculator builds.
PaymentP × r ÷ (1 − (1 + r)−n)
- P
- the amount borrowed
- r
- the interest rate per period: the annual rate divided by the number of payments a year
- n
- the total number of payments
For a monthly loan the rate per period is the annual rate divided by 12; for biweekly payments divide by 26, for weekly by 52. At 0% the formula divides by zero, so the payment is simply the amount divided by the number of payments.
The schedule then applies the same three lines to every period, and the total interest is the sum of the interest lines:
interestbalance × r
principalpayment − interest
new balancebalance − principal
- balance
- what is still owed at the start of the period
Worked example
| Item | Amount | How it is obtained |
|---|---|---|
| Amount borrowed, P | $20,000.00 | Loan amount |
| Rate per period, r | 0.58333% | 7% ÷ 12 monthly payments |
| Number of payments, n | 60 | 5 years × 12 |
| Growth factor, (1 + r)n | 1.41763 | 1.005833360 |
| Discount factor, 1 − (1 + r)−n | 0.29460 | 1 − 1 ÷ 1.41763 |
| Monthly payment | $396.02 | 20,000 × 0.0058333 ÷ 0.29460 |
The first payment then splits as follows, and the schedule repeats the split 59 more times:
| Item | Amount | How it is obtained |
|---|---|---|
| Interest in month 1 | $116.67 | 20,000 × 0.58333% |
| Principal in month 1 | $279.35 | 396.02 − 116.67 |
| Balance after month 1 | $19,720.65 | 20,000 − 279.35 |
| Total of all 60 payments | $23,761.48 | sum of the schedule, final payment adjusted by rounding |
| Total interest | $3,761.48 | 23,761.48 − 20,000 |
The formula total shown under the table, 60 × the unrounded payment of 396.0239 − 20,000, is $3,761.44. The four-cent difference is rounding: each month's interest is rounded to the cent, and the final payment settles whatever is left.
| Item | Amount | How it is obtained |
|---|---|---|
| Monthly payment | $1,199.10 | 200,000 × 0.005 ÷ (1 − 1.005−360) |
| Total interest, no extra payment | $231,677 | 360 payments |
| Payments with $200 extra | 252 | nine years early, instead of 360 |
| Total interest with $200 extra | $151,876 | 252 payments |
| Interest saved | $79,801 | 231,677 − 151,876 |
Reading the result
The headline is the regular payment. Beside it sit the total paid, the total interest and the payoff date, and under those the schedule.
Switch between By year and Every payment above the table. The yearly view is the quickest way to see the shape of the loan: interest falls each year while the principal portion grows. A year row adds up its payments to the cent, so the years foot to the totals above the table. The per-payment view shows every line the way a lender's statement would, including the running balance. The CSV download exports whichever view is on screen.
Two details are worth knowing. The last payment is rarely identical to the others. Because each payment is rounded to the cent, a few cents of rounding accumulate over the term, and the final payment settles the exact remaining balance. There are two totals for interest. The figure beside the table is the sum of the rounded interest lines, which is what you would actually pay. Under the table is the formula total that most other calculators headline, payment × number of payments − amount borrowed. They differ by less than a dollar on typical loans.
What changes the result
How extra payments change the loan
Extra payments go straight to principal, so every one of them reduces the balance on which the next period's interest is charged. Try the same loan with and without an extra payment and compare the interest saved and the final payment date.
Before you overpay, check two things with your lender: that extra payments are applied to principal rather than held as a prepayment of next month's instalment, and whether an early-repayment charge applies. Most personal loans and US mortgages allow penalty-free prepayment, but some fixed-rate products do not.
Monthly, biweekly or weekly
Changing the frequency recalculates a true payment for that schedule: 26 biweekly or 52 weekly payments a year. Total interest is slightly lower than monthly because the balance is reduced a little sooner each month, but the difference is modest.
| Frequency | Payments a year | Payment | Total interest on $200,000 at 6% for 30 years |
|---|---|---|---|
| Monthly | 12 | $1,199.10 | $231,677 |
| Biweekly | 26 | $553.17 | $231,464 |
| Weekly | 52 | $276.53 | $231,370 |
The well-known "biweekly trick" that saves far more is a different thing: paying half your monthly payment every two weeks. Because there are 26 half-payments a year, you make the equivalent of 13 monthly payments instead of 12, and that thirteenth payment is what shortens the loan. To model it, keep the frequency on monthly and enter one-twelfth of your payment as the extra payment.
The term
A longer term lowers the payment and raises the total interest, because the balance stays higher for longer. Run the same amount at two or three terms and compare the total interest line rather than the payment.
What is not included
- Fees and APR. Use the contractual interest rate to estimate the payment. APR can include arrangement fees and other charges, so substituting APR can produce the wrong instalment. Add fees separately when comparing the total cost of offers. The Consumer Financial Protection Bureau explains the distinction.
- Variable rates. The rate is assumed fixed for the whole term. For a variable or tracker loan, run the calculator at a few rates to see the range of payments you might face.
- Insurance and add-ons. Payment-protection or credit insurance is a separate cost.
- Daily interest. This model charges interest once per payment period. A daily-interest loan can give a different interest split or payoff balance depending on payment dates and the lender's day-count convention, even when the scheduled payment is fixed.
Using the result
The payment is the number that has to fit your budget every period without fail. The total interest is the number that tells you what the loan really costs, and the one to compare across offers with different terms: a longer term lowers the payment but almost always raises the total interest. If you are choosing between offers, put each one through the calculator with the same amount and compare total interest side by side, then decide how much a lower payment is worth to you.