Sign a mortgage, a car loan, or a personal loan, and your monthly payment is computed by the same elegant formula. Understanding it changes how you borrow: you'll see why a "small" rate cut saves thousands, why shorter terms crush interest, and why extra payments are so powerful.
A house with a money bag and payment calendar
The anatomy of a payment
Every loan has three ingredients: the principal (amount borrowed), the rate, and the term (number of payments). Your monthly payment is fixed by an equation that balances two things: the lender must earn interest on the remaining balance every month, and the loan must be exactly paid off by the final payment.
The result is the classic amortization formula:
M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]
where M is the monthly payment, P the principal, r the monthly rate (annual rate ÷ 12), and n the total number of payments.
A worked example
Borrow $300,000 at 6.5% for 30 years:
- Monthly rate: 6.5% ÷ 12 = 0.005417
- Payments: 30 × 12 = 360
- Monthly payment: about $1,896
- Total repaid: $682,600 — of which $382,600 is pure interest
That last line is the one lenders don't put on the poster. Over 30 years, interest nearly doubles the price of the house.
Why small rate changes matter so much
Because interest compounds across hundreds of payments, tiny rate differences create enormous totals. At 6.0% instead of 6.5%, the same loan costs $1,798 per month and $347,500 total interest — about $35,000 saved from half a percentage point. This is why shopping for a rate matters more than haggling over the house price.
The term trade-off
- Shorter term (15 years): higher payment, but interest for 15 fewer years. The $300,000 loan at 6.5% costs ~$2,655/month but only ~$178,000 in interest — saving over $200,000.
- Longer term (30 years): lower, safer payment — but you pay for the breathing room.
There's no universally right answer. The right term is the one that fits your cash flow and your discipline: a 30-year loan with extra payments can beat a 15-year loan you can't sustain.
Extra payments: the hack inside the formula
The formula assumes fixed payments. Pay extra, and every extra dollar hits the principal directly, which removes all future interest that dollar would have generated. Adding just $100/month to the 30-year example pays it off about 3.5 years early and saves roughly $47,000. Check your loan has no prepayment penalty first.
What lenders won't always tell you
- Compare APR, not headline rate — APR folds fees into the true cost.
- Watch the amortization schedule — early payments are mostly interest, so refinancing late in a loan resets the interest clock.
- Shorter terms often get lower rates — the discount is built into pricing.
Run your own numbers before you ever sit at a signing table:
Loan & Mortgage Calculator
Estimate monthly payments, total interest and overall cost for any fixed-rate loan.
Enter the loan amount, rate and term to see your payment breakdown.
Ready to make the extra payments work for you? See how a savings plan grows in The Power of Compound Interest.
