Every loan payment is calculated using the same formula — whether it’s a $2,000 personal loan or a $500,000 mortgage. Understanding the formula lets you verify lender numbers, model scenarios before you apply, and understand exactly what drives your payment amount.
Quick Answer
The monthly loan payment formula is:
Payment = P × [r(1+r)^n] / [(1+r)^n − 1]
Where:
- P = loan principal (amount borrowed)
- r = monthly interest rate = annual rate ÷ 12
- n = total number of monthly payments = years × 12
You don’t need to compute this by hand — the Loan Calculator does it instantly. But knowing the formula tells you which variables drive your payment: principal (P), rate (r), and term (n). Change any of these and you change your payment.
Breaking Down the Formula
The formula derives from the mathematical requirement that a fixed payment over n months, after paying monthly interest on the declining balance, results in a balance of exactly zero.
Each component:
r (monthly rate): Convert your annual APR to a monthly rate by dividing by 12.
- 9% APR → r = 0.09 ÷ 12 = 0.0075
- 6% APR → r = 0.06 ÷ 12 = 0.005
n (number of payments): Multiply years by 12.
- 3 years → n = 36
- 5 years → n = 60
- 30 years → n = 360
Worked examples below show the formula applied to common loan scenarios.
Example 1: Personal Loan
$15,000 at 9% APR for 36 months
- P = 15,000
- r = 0.09 ÷ 12 = 0.0075
- n = 36
Payment = 15,000 × [0.0075 × (1.0075)^36] / [(1.0075)^36 − 1]
= 15,000 × [0.0075 × 1.3086] / [1.3086 − 1]
= 15,000 × 0.009815 / 0.3086
= 15,000 × 0.031802
= $477/month
Total paid: $477 × 36 = $17,172 Total interest: $17,172 − $15,000 = $2,172
Example 2: Auto Loan
$28,000 at 7% APR for 60 months
- P = 28,000
- r = 0.07 ÷ 12 = 0.005833
- n = 60
Payment = 28,000 × [0.005833 × (1.005833)^60] / [(1.005833)^60 − 1]
= 28,000 × [0.005833 × 1.4176] / [1.4176 − 1]
= 28,000 × 0.008269 / 0.4176
= 28,000 × 0.019799
= $554/month
Total paid: $554 × 60 = $33,240 Total interest: $33,240 − $28,000 = $5,240
Example 3: Mortgage
$250,000 at 6.5% APR for 30 years
- P = 250,000
- r = 0.065 ÷ 12 = 0.005417
- n = 360
Payment = 250,000 × [0.005417 × (1.005417)^360] / [(1.005417)^360 − 1]
= 250,000 × [0.005417 × 6.8485] / [6.8485 − 1]
= 250,000 × 0.037093 / 5.8485
= 250,000 × 0.006342
= $1,580/month
Total paid: $1,580 × 360 = $568,800 Total interest: $568,800 − $250,000 = $318,800
This is why mortgage rates matter enormously. A 1% rate increase on a $250,000 mortgage adds approximately $150/month and $54,000 in total interest over 30 years.
How Each Variable Affects the Payment
Loan amount (P): payment scales linearly. Double the loan amount → double the payment (at same rate and term).
Interest rate (r): roughly $5–10/month per percentage point per $10,000 borrowed (for a 5-year term).
| Rate | Payment on $20,000/5yr | Payment on $200,000/30yr |
|---|---|---|
| 5% | $377 | $1,074 |
| 6% | $387 | $1,199 |
| 7% | $396 | $1,331 |
| 8% | $406 | $1,468 |
| 10% | $425 | $1,755 |
Loan term (n): longer term → lower payment, higher total interest.
| Term | Payment on $20,000 at 8% | Total Interest |
|---|---|---|
| 24 months | $905 | $1,720 |
| 36 months | $627 | $2,572 |
| 48 months | $488 | $3,424 |
| 60 months | $406 | $4,360 |
| 84 months | $322 | $7,048 |
Using the Formula Practically
Verify lender numbers: if a lender quotes you a payment, check it against the formula using the stated rate and term. If the numbers don’t match, ask about fees that may be rolled into the principal.
Compare offers: two different rates and terms can look similar by payment but differ dramatically in total cost. Run both through the formula and compare total interest paid.
Model extra payments: the formula calculates the fixed scheduled payment. Extra payments reduce the principal, shortening the remaining n and cutting total interest — the Loan Calculator models this.
Plan before applying: know your maximum comfortable payment and work backward. If you can afford $450/month at 8% over 48 months, the maximum loan is approximately $18,800. Apply for that amount — not what the lender says you qualify for.
Use the Loan Calculator to run any scenario instantly — amount, rate, and term — without working through the formula manually.