How your loan payment is calculated
Personal loans and auto loans are amortizing loans: you pay the same amount every month, and each payment covers that month’s interest first and pays down principal with the rest. The payment comes from this formula:
payment = P × r ÷ (1 − (1 + r)^−n)
P: the amount you borrow.r: the monthly rate, your annual rate divided by 1,200.n: the number of monthly payments (5 years is 60).
For example, $20,000 at 9% for 5 years is $415.17 a month. Over 60 payments you repay the $20,000 plus $4,910.03 in interest.
Interest rate vs. APR
The interest rate leaves out fees. The APR builds them in, which is why the Truth in Lending Act requires lenders to show it and why it’s the right number for comparing offers.
Add a 3% origination fee to the example and $600 comes off the top. Your payment stays at $415.17, but you’re paying it on $19,400 of real money, so the APR rises from 9% to 10.31%.
Shorter vs. longer terms
The same $20,000 at 9% with a 3% origination fee:
| Term | Payment | Total interest | APR |
|---|---|---|---|
| 36 months | $635.99 | $2,895.81 | 11.09% |
| 60 months | $415.17 | $4,910.03 | 10.31% |
The APR looks better on the longer loan because the fee is spread over more years, but you still pay about $2,000 more in interest.
Auto loans: 60 vs. 72 months
Longer auto loans have become common because they make a car look affordable. On $35,000 at 7%:
- 60 months: $693.04 a month and $6,582.52 in interest.
- 72 months: $596.72 a month and $7,963.50 in interest.
The extra year saves about $96 a month and costs about $1,381 more. It also keeps you owing more than the car is worth for longer, which hurts if you sell or total it. To see the full cost of owning the car, try the car cost calculator.
Before you sign
- Compare APRs, not monthly payments.
- Ask whether the origination fee is taken out of the loan proceeds.
- Check the agreement for a prepayment penalty.
- If you’re buying a home instead, use the mortgage calculator, which adds extra payments and a full amortization schedule.
What this calculator doesn’t include
It assumes a fixed rate, equal monthly payments and a fee paid at signing. It doesn’t include credit insurance, late fees or sales tax on a car. Your lender’s APR may differ slightly if other finance charges apply.