Before you take out a car loan, mortgage, or personal loan, it pays to know exactly what the monthly payment will be — and how much interest you'll hand over by the end. There's one standard formula that lenders use, and once you see it broken down, it's not nearly as intimidating as it looks.
The amortized loan payment formula
A fixed-rate loan is paid off in equal monthly installments. Each payment covers the interest due that month plus a chunk of the principal. The formula is:
M = P × [ r(1 + r)^n ] ÷ [ (1 + r)^n − 1 ]
Where:
- M = monthly payment
- P = loan principal (the amount you borrow)
- r = monthly interest rate = annual rate ÷ 12
- n = total number of monthly payments = years × 12
A full worked example
Suppose you borrow $20,000 at a 6% annual rate over 5 years.
Step 1 — Find the monthly rate:
- r = 0.06 ÷ 12 = 0.005
Step 2 — Find the number of payments:
- n = 5 × 12 = 60
Step 3 — Plug into the formula:
- (1 + r)^n = (1.005)^60 ≈ 1.348850
- Numerator: r × (1+r)^n = 0.005 × 1.348850 = 0.00674425
- Denominator: (1+r)^n − 1 = 1.348850 − 1 = 0.348850
- M = 20,000 × (0.00674425 ÷ 0.348850) ≈ 20,000 × 0.0193328 ≈ $386.66
So your monthly payment is about $386.66.
Total interest and total cost
To see the true cost of the loan, multiply the payment by the number of months, then subtract the principal:
- Total paid = M × n = $386.66 × 60 = $23,199.60
- Total interest = Total paid − P = $23,199.60 − $20,000 = $3,199.60
That interest figure is the headline number worth shopping around to reduce. Lowering the rate or shortening the term both cut it down.
How to use it
The exponents make this awkward to do by hand, so let the Loan Calculator handle it. Enter the loan amount, annual interest rate, and term in years, and it returns your monthly payment, total interest, and total cost over the life of the loan.
A few tips:
- Shorter terms mean higher monthly payments but far less total interest.
- Extra payments toward principal shrink the balance and reduce interest faster than the schedule assumes.
Curious how the interest itself accumulates? The Interest Calculator is great for that. And to check whether a payment fits your budget, run your pay through the Salary Converter to see your real monthly take-home.