To calculate a car loan EMI (the equated monthly installment you pay until the balance hits zero), use the formula E = P × r × (1 + r)n / ((1 + r)n – 1), where P is the amount you are financing, r is the monthly interest rate written as a decimal, and n is the total number of monthly payments. On a $25,000 loan at 6% annual interest over five years, the formula produces a payment of about $483 per month. The math is straightforward once the inputs are correct, and getting those inputs right matters more than the arithmetic itself.
The Three Inputs You Need
Every EMI calculation uses exactly three numbers: the loan principal, the annual interest rate, and the term in months. All three appear on the loan estimate or Truth in Lending Act (TILA) disclosure your lender must give you before you sign. That document shows the amount financed, the annual percentage rate (APR), and the payment schedule.1Federal Deposit Insurance Corporation (FDIC). V-1 Truth in Lending Act (TILA)
One detail to watch. The “amount financed” on the TILA disclosure is not always identical to the sticker price minus your down payment. The FDIC defines it as the net amount of credit extended for your use, which excludes certain prepaid finance charges.2Federal Deposit Insurance Corporation (FDIC). V-1 Truth in Lending Act (TILA) – Section: Amount Financed For your calculation, use the actual dollar amount you are borrowing. If you are financing $25,000 after your down payment and trade-in, that is your P.
The APR reflects the total yearly cost of borrowing, including fees beyond the base interest rate.3Federal Deposit Insurance Corporation (FDIC). V-1 Truth in Lending Act (TILA) – Section: Annual Percentage Rate For the formula, convert that annual rate into a monthly decimal: divide by 12, then divide by 100. A 6% annual rate becomes 6 ÷ 12 = 0.5%, and 0.5 ÷ 100 = 0.005. That 0.005 is your r.
The term just has to be in months. A five-year loan is 60 months; a six-year loan is 72. That number is your n.
The Formula, Piece by Piece
The formula looks dense but does one job: it finds the fixed payment that will erase the entire balance, including compounded interest, by the final month.
E = P × r × (1 + r)n / ((1 + r)n – 1)
- P = the amount borrowed
- r = the monthly interest rate as a decimal
- n = the total number of monthly payments
The (1 + r)n piece accounts for how interest compounds each month. Multiplying it by P and r in the numerator captures the total growth of the debt. The denominator subtracts one from that same compounding factor, scaling the result down to a single monthly slice. The output is a payment that stays identical every month, even though the split between interest and principal shifts over time.
Worked Example: $25,000 at 6% for Five Years
Numbers make it stick. Here is every step for a $25,000 loan at 6% annual interest over 60 months.
Step 1. Convert the rate. 6% annual ÷ 12 = 0.5% monthly. As a decimal, r = 0.005.
Step 2. Set n. Five years × 12 months = 60.
Step 3. Calculate (1 + r)n. Add 1 to the monthly rate: 1 + 0.005 = 1.005. Raise to the 60th power: 1.00560 = 1.34885. Keep this number handy; it appears twice.
Step 4. Solve the numerator. 25,000 × 0.005 × 1.34885 = 168.61.
Step 5. Solve the denominator. 1.34885 – 1 = 0.34885.
Step 6. Divide. 168.61 ÷ 0.34885 = $483.32 per month.
That is your EMI for the life of the loan. Change any input and the payment changes. Push the rate to 7% and the same loan runs $495.03 per month. Shorten the term to 48 months at 6% and the payment jumps to $587.13, though you pay far less interest overall.
Using a Spreadsheet Instead
Raising numbers to the 60th power by hand is tedious. Excel and Google Sheets both have a built-in PMT function that runs the same formula. The syntax is identical in both:
=PMT(rate, nper, pv)
- rate = monthly interest rate (annual rate ÷ 12, as a decimal)
- nper = total number of payments
- pv = present value (the loan amount, entered as a positive number)
For the example above, type =PMT(0.06/12, 60, 25000) and press Enter. The result comes back as a negative number (about –483.32) because spreadsheets treat outgoing payments as negative cash flows. That is a display convention, not an error.4Microsoft Support. PMT Function Wrap the formula in ABS() or multiply by –1 to flip it positive.
Google Sheets uses the same function name and argument order.5Google. PMT – Google Docs Editors Help PMT also takes two optional arguments: a future value (usually 0 for a standard payoff) and a timing flag (0 for end-of-month payments, 1 for beginning). Most auto loans use end-of-period payments, so leaving both blank gives the right answer.
The real advantage is speed. Changing the rate from 6% to 5.5%, or the term from 60 to 72 months, takes one keystroke, and you can compare scenarios side by side.
Total Interest Over the Life of the Loan
To find total borrowing cost, multiply the EMI by the number of payments. For the example: $483.32 × 60 = $28,999.20. Subtract the original loan amount, and total interest is $3,999.20.
This is the number that matters most when comparing offers. A dealer might advertise a lower monthly payment by stretching the term to 72 months, which drops the EMI to roughly $414 at the same 6% rate. That looks better until you multiply out: $414 × 72 = $29,808, or about $4,808 in interest. The longer loan costs $800 more in interest for a monthly savings of about $69.
How the Term Shifts the Answer
Loan length is the biggest lever on both your monthly payment and your total interest. Here is the same $25,000 loan at 6% across common auto terms:
- 36 months: EMI ≈ $760. Total interest ≈ $2,360.
- 48 months: EMI ≈ $587. Total interest ≈ $3,176.
- 60 months: EMI ≈ $483. Total interest ≈ $3,999.
- 72 months: EMI ≈ $414. Total interest ≈ $4,808.
- 84 months: EMI ≈ $365. Total interest ≈ $5,660.
Moving from a three-year to a seven-year loan nearly halves the monthly payment but more than doubles total interest.
Fees That Change Your P
The formula only gives the right answer if you feed it the true amount you are financing, and that number is often larger than the car’s price minus your down payment. Costs commonly rolled into the loan principal include:
- Sales tax. State vehicle sales tax ranges from 0% to over 8%, and local surcharges can push it higher. On a $30,000 car in a 6% state, that is $1,800 added to the financed amount if you don’t pay it upfront.
- Dealer documentation fees. Processing charges run from around $50 to over $800 depending on the state. About a third of states cap these fees; the rest let dealers set their own.
- Registration and title fees. One-time state fees for registering and titling a vehicle range from about $20 to over $700, depending on the state and the vehicle’s value or weight.
- Add-on products. Extended warranties, GAP insurance, and paint protection plans are often financed. A $2,000 extended warranty rolled into a 60-month loan at 6% adds roughly $39 per month and about $320 in additional interest.
Add up every fee being financed before running your calculation. That total is your real P. Dealers sometimes quote a monthly payment based on the vehicle price alone, then present a higher number once the paperwork includes the extras. Running the formula yourself catches that before you sign.
One Boundary: Simple vs. Precomputed Interest
The formula above assumes simple interest, which is how most auto loans work. With simple interest, the lender calculates what you owe based on your actual outstanding balance each period. Pay down principal early, and the interest charged the following month drops.6Consumer Financial Protection Bureau. What’s the Difference Between a Simple Interest Rate and Precomputed Interest on an Auto Loan
Some lenders use precomputed interest instead. With that method, all the interest you will owe over the full term is calculated upfront and built into the payment schedule. Extra payments on a precomputed loan do not reduce the interest you owe, because the total was already locked in.6Consumer Financial Protection Bureau. What’s the Difference Between a Simple Interest Rate and Precomputed Interest on an Auto Loan Check your loan agreement. The EMI formula still gives the correct monthly payment either way, but the plan of paying extra to save on interest only works with simple interest.