How to calculate a loan payment
This page shows how to calculate a loan payment by hand, with a worked example, and gives you a calculator that confirms the result and shows the full schedule.
Amortization schedule
| Year | Principal | Interest | Balance |
|---|---|---|---|
| 1 | $4,607.09 | $1,033.51 | $10,392.91 |
| 2 | $4,989.47 | $651.13 | $5,403.44 |
| 3 | $5,403.44 | $236.99 | $0.00 |
Step by step
Take a $15,000 loan at 8% for 36 months. Step one: the monthly rate is 0.08 ÷ 12 = 0.006667. Step two: compute (1 + 0.006667)^−36, which is about 0.7873. Step three: the denominator is 1 − 0.7873 = 0.2127. Step four: the payment is 15,000 × 0.006667 ÷ 0.2127 = $470.05.
Over 36 payments you repay $16,921.64, which means $1,921.64 of interest. The first month’s interest is $15,000 × 0.006667 = $100, so $370.05 goes to principal.
Variations
If the rate is 0%, divide the amount by the number of months. If you make extra payments, the formula still gives the required payment; the schedule just ends sooner. If a lender includes fees in the amount financed, use that amount rather than the amount you receive.
$15,000 at 8% by loan length
Borrowing $15,000 at 8% over 3 years costs $470.05 a month and $1,922 in interest, $16,922 in total. Shorter terms raise the payment but cut the interest, and longer terms do the reverse. The table shows the trade-off across common terms.
| Term | Monthly payment | Total interest | Total paid |
|---|---|---|---|
| 12-month | $1,304.83 | $658 | $15,658 |
| 2-year | $678.41 | $1,282 | $16,282 |
| 3-year | $470.05 | $1,922 | $16,922 |
| 4-year | $366.19 | $2,577 | $17,577 |
| 5-year | $304.15 | $3,249 | $18,249 |
| 7-year | $233.79 | $4,639 | $19,639 |
| 10-year | $181.99 | $6,839 | $21,839 |
How your rate changes the cost
Personal loan rates vary widely with credit score, from the mid single digits for strong borrowers to 30% or more for weak credit. On $15,000 over 3 years, moving from 8% to 11% adds $757 in interest.
| APR | Monthly payment | Total interest |
|---|---|---|
| 5% | $449.56 | $1,184 |
| 6.5% | $459.74 | $1,550 |
| 8% | $470.05 | $1,922 |
| 9.5% | $480.49 | $2,298 |
| 11% | $491.08 | $2,679 |
How much can you borrow for a given payment?
Working backwards at 8% over 3 years, here is the loan size each monthly payment supports.
| Monthly payment | Loan amount |
|---|---|
| $200/month | $6,382 |
| $300/month | $9,574 |
| $400/month | $12,765 |
| $500/month | $15,956 |
When is half of a $15,000 loan repaid?
With a $470.05 payment, the balance falls below half ($7,500) after 20 payments, about 1.7 years into a 3 years loan. Because interest is highest at the start, the second half of the loan is paid down much faster than the first.
| After | Balance left | Paid so far |
|---|---|---|
| 1 year | $10,393 | $5,641 |
| 2 years | $5,403 | $11,281 |
Frequently asked questions
How do I calculate a loan payment in Excel?
Use =PMT(rate/12, months, -amount). For the example above, =PMT(0.08/12, 36, -15000) returns 470.05.
Why is the lender’s payment different?
Fees financed into the loan, daily interest or a first payment that is not exactly one month away can change it slightly.
How is a loan payment calculated?
The payment is principal × r ÷ (1 − (1 + r)^−n), where r is the monthly rate (APR ÷ 12) and n is the number of months. Each payment covers that month’s interest first, and the rest reduces the balance.
What is the difference between interest rate and APR?
The interest rate is the cost of borrowing the money. APR also includes certain fees, so it is the better number for comparing offers. This calculator treats the rate you enter as the rate that accrues on the balance.
Related calculators
Estimates from standard loan formulas, not a loan offer or financial advice. Example rates are assumptions: use your own quote.