PmtCalcHow the monthly payment is calculated
A fixed-rate installment loan uses one level payment for its whole life. Early on, most of each payment goes to interest. As the balance falls, more goes to principal. The payment comes from this formula:
Payment = P × r / (1 − (1 + r)−n)
Here P is the amount borrowed, r is the monthly rate (annual rate ÷ 12) and n is the number of monthly payments. At a 0% rate the payment is simply P ÷ n.
Example
Borrow $25,000 at 7.5% for 5 years. The monthly rate is 0.625% and there are 60 payments, so the payment is $500.95. Over five years you pay $30,056.96: the $25,000 you borrowed plus $5,056.96 of interest.
What changes the payment most
- Term. A longer term lowers the payment but raises total interest, often sharply.
- Rate. Each percentage point adds more to the payment the longer the term.
- Amount. The payment scales directly with the amount borrowed: borrow 10% less and the payment is 10% lower.
Frequently asked questions
Does this payment include fees or insurance?
No. It is principal and interest only. Fees deducted from the loan raise its true cost, which shows up in the APR. Use the APR calculator to include them, or the mortgage calculator to add taxes, insurance and PMI.
Why is so much of my early payment interest?
Interest is charged on the remaining balance, which is largest at the start. As you pay the balance down, the interest portion shrinks and the principal portion grows. The amortization schedule shows this payment by payment.
Is the result exact?
The payment is rounded to the cent the way lenders do, and the final payment is adjusted so the balance ends at exactly zero. Your lender’s numbers can differ slightly if they use daily interest or a different first-payment date.
How do I pay less interest?
Choose a shorter term, get a lower rate, or pay extra toward principal. The extra payment calculator shows how much each option saves.
Sources
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