One formula covers most loans
Personal loans, car loans and mortgages with a fixed rate all use the same math. The lender picks a single monthly payment that covers each month's interest and leaves just enough principal to hit zero on the last payment. That's called amortization.
You need three numbers: the amount borrowed (P), the monthly interest rate (r) and the number of payments (n). The monthly rate is the annual rate divided by 12.
Formula notes
Payment = P x r / (1 - (1 + r)^(-n))
A worked example
Say you borrow $10,000 at 8.5% for 5 years. The monthly rate is 0.085 / 12, about 0.0070833. There are 60 payments. Put those into the formula and the payment is $205.17.
Multiply by 60 and you repay $12,309.92. Take away the $10,000 you borrowed and $2,309.92 is interest. In a spreadsheet, =PMT(0.085/12, 60, -10000) returns the same $205.17.
Why early payments are mostly interest
Each month, interest is the balance times the monthly rate. In month one that's $10,000 x 0.0070833, or $70.83. The rest of the $205.17, $134.33, pays down the loan.
Next month the balance is a bit lower, so interest is a bit lower and principal a bit higher. By the final year, almost all of each payment goes to principal. This is why paying extra early saves more than paying extra late: it removes balance that would have been charged interest for years.
Term length: the trade-off
Stretching the term lowers the payment and raises the total cost. The same $10,000 at 8.5% costs $315.68 a month over 3 years with $1,364.31 of interest. Over 7 years it's $158.36 a month with $3,302.65 of interest.
Lenders often quote higher rates for longer terms, which widens the gap further. Pick the shortest term whose payment you can carry comfortably, and keep some room for surprises.
Fees and the true cost
An origination fee changes the math in a way the payment alone hides. If a $300 fee is taken out of a $10,000 loan, you get $9,700 but repay the whole $10,000 plus interest. Your real cost is everything you pay minus what you received: $12,309.92 minus $9,700, or $2,609.92.
This is also why APR exists. It folds required fees into a yearly rate so offers can be compared on one number. Use the contract rate for the payment and APR for comparing.
Loans that follow different math
Not every loan amortizes evenly. An interest-only loan charges only interest for a set period, so the balance doesn't fall until regular payments begin. A balloon loan keeps payments low and leaves a large lump sum due at the end. A variable-rate loan resets the payment when the rate changes.
For those, the standard formula only describes one stretch of the loan. Ask the lender for the full payment schedule and read the terms on rate changes before you sign.
Run your own numbers
Hand math is good for checking, but a schedule with fees and extra payments takes a long time on paper. Our loan calculator handles fee treatment, monthly and one-time extra payments, and shows the month-by-month balance. Enter two offers one after the other and compare total borrowing cost rather than the payment.
Frequently asked questions
How do I calculate a loan payment in Excel?
Use =PMT(annual rate/12, number of months, -loan amount). For $10,000 at 8.5% over 5 years, =PMT(0.085/12, 60, -10000) returns $205.17.
How is interest calculated on each loan payment?
Multiply the remaining balance by the monthly rate. On a $10,000 balance at 8.5%, that's $10,000 x 0.085 / 12 = $70.83 for the first month.
What does amortization mean?
It means paying a loan off with equal scheduled payments that each cover that month's interest plus some principal, so the balance reaches zero at the end of the term.
How do I work out the total cost of a loan?
Add up everything you'll pay, including upfront fees, then subtract the cash you actually received. What's left is the true cost of borrowing.
Does paying extra early save more than paying extra late?
Yes. Money paid early removes balance that would have built interest for many more months. A dollar of extra principal in month one saves more than a dollar in the final year.
References
These sources support the method or guidance used for Loan Calculator. Verify time-sensitive rules at the source.
Try the calculator
Open Loan Calculator, enter your scenario, and compare its supporting rows with this guide's method and checks.