How a loan’s monthly payment is calculated
Most loans, from car loans to personal loans and mortgages, are repaid in equal monthly payments. Each payment covers that month’s interest, and the rest pays down the loan. Here’s how the payment is worked out, and what changes it.
The formula
Payment = P × r × (1 + r)n ÷ ((1 + r)n − 1)
- P is the amount borrowed.
- r is the monthly interest rate: the yearly rate divided by 12, as a decimal. 9% a year is 0.0075 a month.
- n is the number of monthly payments.
With no interest, the payment is simply the amount divided by the number of months.
A worked example
Take $20,000 borrowed at 9% a year, repaid over five years, which is 60 payments.
- The monthly rate is 9% ÷ 12 = 0.75%, or 0.0075.
- (1 + 0.0075)60 = 1.565681.
- Payment = 20,000 × 0.0075 × 1.565681 ÷ 0.565681 = $415.17.
Over 60 payments you pay $24,909.99: the $20,000 you borrowed and $4,909.99 in interest. The last payment is a few cents smaller, $414.96, because each month’s interest is rounded to the cent.
Where each payment goes
In the first month you owe the full $20,000, so the interest is $20,000 × 0.0075 = $150.00 and the other $265.17 pays down the loan. In the second month you owe $19,734.83, so the interest is $148.01 and $267.16 goes to the loan. Every month, a little more of the same payment goes to the loan. Year by year:
| Year | Paid | Interest | Loan paid down | Left to pay |
|---|---|---|---|---|
| 1 | $4,982.04 | $1,665.40 | $3,316.64 | $16,683.36 |
| 2 | $4,982.04 | $1,354.29 | $3,627.75 | $13,055.61 |
| 3 | $4,982.04 | $1,013.97 | $3,968.07 | $9,087.54 |
| 4 | $4,982.04 | $641.74 | $4,340.30 | $4,747.24 |
| 5 | $4,981.83 | $234.59 | $4,747.24 | $0.00 |
How the term changes the cost
The same $20,000 at 9%, over three, five and seven years:
| Term | Monthly payment | Total interest | Total paid |
|---|---|---|---|
| 3 years | $635.99 | $2,895.82 | $22,895.82 |
| 5 years | $415.17 | $4,909.99 | $24,909.99 |
| 7 years | $321.78 | $7,029.73 | $27,029.73 |
A longer term makes each payment smaller and the loan more expensive: seven years costs more than twice the interest of three.
Paying extra
An extra payment goes straight to the balance, so all the interest after it is charged on less. On the same loan, paying an extra $2,000 at the end of the first year, and keeping the monthly payment at $415.17, finishes the loan six months early and saves $801.38 in interest. Check first whether your lender charges a fee for repaying early.
Lending to someone you know
The same maths works for a loan between friends or family. Agree the amount, the rate (or none) and the number of months, and you have a fair, fixed monthly payment that pays it off exactly. Try your own numbers in the loan calculator.
In ClearOwe, an instalment loan needs just two numbers: give it the monthly payment and how long it runs, or the amount and the rate, and it works out the rest and shows what’s left after each payment.
Common questions
Why is most of an early payment interest?
Interest is charged on what you still owe. At the start you owe the most, so more of each payment goes to interest. As the balance falls, more of the same payment goes to the loan itself.
Does a longer loan term cost more?
Yes. It lowers the monthly payment but raises the total interest. On a $20,000 loan at 9%, stretching it from five years to seven cuts the payment from $415.17 to $321.78 but adds about $2,120 in interest.
Is it worth paying a loan off early?
Usually, if there’s no fee for repaying early and you don’t need the money for something more pressing. Extra payments go straight to the balance, so every later payment carries less interest.
What is an amortization schedule?
A table of every payment, split into interest and the part that pays down the loan, with the balance left after each one. It shows exactly how a loan is paid off over time.