Loan payment formula, explained (with examples)

Most installment loans (personal loans, auto loans, many student loans) are modeled with a standard amortization formula. “Amortization” just means your balance goes down over time because each payment covers two things: interest (the cost of borrowing) and principal (the amount you actually owe). Early in the loan, interest is a larger part of the payment because the balance is high. Later, more of each payment goes to principal because the balance has fallen.

For a loan with principal P, periodic interest rate r, and total number of payments n, the payment per period is:

Payment = P × r ÷ (1 − (1 + r)⁻ⁿ)

Where:

• P = loan amount (principal)
• r = interest rate per payment period (APR ÷ payments per year)
• n = number of payments (term in years × payments per year, or term in months converted)

If the rate is 0%, the formula simplifies to a straight split: Payment = P ÷ n. This calculator automatically handles the 0% case so you don’t get weird divisions by zero.

Suppose you borrow $10,000 at 6% APR for 3 years, paid monthly. Monthly rate r = 0.06 ÷ 12 = 0.005. Number of payments n = 36. Plugging into the formula produces a payment of about $304.22 per month. Over 36 payments, you’ll pay roughly $10,951.92 total, meaning about $951.92 in interest.

If you add an extra $50 per month in Example 1, your balance shrinks faster. That means fewer periods where interest is charged on a high balance. The result is usually: (1) a shorter payoff time and (2) lower total interest. This calculator shows both so you can see whether an extra payment strategy is “worth it” for you.

Biweekly payments happen 26 times per year. When people say “biweekly saves interest,” they usually mean one of two things: (a) you pay more frequently (reducing balance sooner) and (b) many borrowers pay half of the monthly payment every 2 weeks, which effectively creates 13 monthly-equivalent payments per year instead of 12. This calculator models the frequency directly: you choose monthly (12), biweekly (26), or weekly (52).

Upfront fees don’t usually change the amortization formula itself, but they do change what you really paid. If you pay $300 in fees, your “out of pocket” cost is higher. This calculator reports fees separately so you can keep the math clean: payment and interest come from amortization, while fees are added to the overall cost summary.

The amortization preview lists each payment’s split between interest and principal. It’s useful for:

• Understanding why interest is higher early on
• Seeing how extra payments accelerate principal reduction
• Estimating your balance after a certain number of payments

Loan Calculator FAQs

• Is this the same as an APR calculator?

  This page is primarily a payment + amortization calculator. You input APR (or rate) and it computes payment. If you want to compare APR vs APY or estimate APR from fees, use the related tools below.

• Why does my lender’s payment differ slightly?

  Differences come from rounding, daily interest methods, payment timing, compounding rules, and how fees are handled. Small differences are normal; always verify with your official disclosure statement.

• Does extra payment always reduce term?

  Typically yes, if the lender applies the extra amount to principal. Some loans apply extra payments differently, or require you to request “principal-only” payments. Check your lender’s policy.

• Can I use this for credit cards?

  Credit cards are usually revolving debt with minimum-payment rules and compounding that can vary by issuer. For credit cards, use the Credit Card Payoff and Minimum Payment Impact calculators linked below.

• What’s the fastest way to lower interest?

  Two common strategies: (1) reduce the rate (refinance, negotiate, improve credit), and/or (2) reduce the balance faster (extra payments, debt snowball/avalanche strategies). Use the calculators to compare scenarios.