Payment Calculator Calculators

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A payment calculator computes regular loan payments based on principal, interest rate, and loan term. The most common application is calculating monthly mortgage or car loan payments using the PMT (payment) formula. Understanding how loan payments are calculated — and how they split into principal and interest over time through amortization — helps borrowers compare loans, plan budgets, and understand the true cost of borrowing. A small reduction in interest rate or additional payments can dramatically reduce total interest paid over a loan's life.

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Monthly Payment Formula (PMT)

PMT = P × [r(1+r)^n] / [(1+r)^n − 1]

Where:

  • P = principal (loan amount)
  • r = monthly interest rate = annual rate / 12
  • n = total number of payments = years × 12

Worked Example

$300,000 mortgage at 7% annual interest, 30-year term:

r = 0.07/12 = 0.005833/month
n = 30 × 12 = 360 payments
PMT = 300,000 × [0.005833 × (1.005833)^360] / [(1.005833)^360 − 1]
(1.005833)^360 = 8.116
PMT = 300,000 × [0.005833 × 8.116] / [8.116 − 1]
PMT = 300,000 × 0.04734 / 7.116 = $1,995.91/month

Amortization

Each payment is split into interest and principal components:

  • Interest portion = Beginning balance × monthly rate
  • Principal portion = PMT − Interest
  • New balance = Previous balance − Principal portion

Early payments are mostly interest; later payments are mostly principal. At 7% over 30 years on $300,000: total interest paid ≈ $418,527.

Effect of Extra Payments

Making one extra principal payment per month reduces the 30-year mortgage above to ~23 years, saving ~$93,000 in interest. Even $100/month extra significantly shortens the loan term.

Tools

Excel: =PMT(rate/12, nper, -pv) gives monthly payment. For the above: =PMT(0.07/12, 360, -300000) = $1,995.91

Glossary

PMT (Payment) Formula
PMT = P × [r(1+r)^n] / [(1+r)^n − 1]. Calculates fixed periodic loan payment from principal P, monthly interest rate r, and total payments n. The standard formula for mortgage and installment loan payments.
Amortization
The process of paying off a loan through regular payments that cover both interest and principal. Early payments are mostly interest; later payments are mostly principal. An amortization schedule shows the split for each payment over the loan's life.
Principal
The original loan amount or the outstanding balance on which interest is calculated. Interest = principal × periodic rate. Extra payments toward principal reduce the balance, decrease future interest charges, and shorten the loan term.

Frequently Asked Questions

PMT = P × [r(1+r)^n] / [(1+r)^n − 1], where P = loan amount, r = monthly rate (annual rate/12), and n = total payments (years × 12). Example: $20,000 car loan at 6% for 5 years: r = 0.06/12 = 0.005; n = 60; PMT = 20,000 × [0.005 × 1.005^60] / [1.005^60 − 1] = 20,000 × 0.00644/0.349 = $386.66/month. In Excel: =PMT(0.06/12, 60, -20000).

An amortization schedule shows how each payment is split between interest and principal over the loan's life. Interest portion = beginning balance × monthly rate. Principal portion = payment − interest. New balance = old balance − principal. Early in the loan, most of each payment is interest; later payments are mostly principal. As principal decreases, the interest portion shrinks — accelerating payoff in later years.

Total interest depends on principal and rate. At 7% on a $300,000 30-year mortgage (monthly payment $1,995.91): total paid = $1,995.91 × 360 = $718,527 total. Total interest = $718,527 − $300,000 = $418,527 — more than the original loan. At 4%: total interest ≈ $215,609. The difference shows why interest rate matters enormously on long-term loans.

Extra principal payments reduce the balance faster, so less interest accrues each month, and more of each subsequent regular payment goes to principal. On a $300,000 30-year mortgage at 7%, an extra $200/month toward principal reduces the term to ~25 years and saves ~$85,000 in interest. Lump-sum payments (annual tax refund) have similar impact. Always specify payments go to principal, not future payments, and confirm there is no prepayment penalty.