$1,580.17
$568,861.22
$318,861.22
127.5%
$1,580.17
$568,861.22
$318,861.22
127.5%
The Payment Calculator (PMT) computes the periodic payment required to fully amortize a loan or fund a future value through equal installments. This is the standard formula used by banks, mortgage companies, and auto dealers to determine your monthly payment on any fixed-rate loan.
The PMT formula is derived from the present value of annuity equation, solved for the payment amount: PMT = PV × r / (1 - (1 + r)-n), where PV is the loan principal, r is the per-period interest rate, and n is the total number of payments. This formula ensures that each payment covers both interest on the remaining balance and a portion of the principal, resulting in the loan being fully paid off by the final payment.
Understanding how PMT calculations work empowers borrowers to make better financial decisions. For a $250,000 mortgage at 6.5% over 30 years, the monthly payment is $1,580.17 — but the total amount paid over the life of the loan is $568,861, meaning you pay $318,861 in interest alone. That's more than the original loan amount! Shortening the term to 15 years raises the monthly payment to $2,177.77 but reduces total interest to $141,998 — a savings of $176,863.
The interest-to-principal ratio reveals the true cost of borrowing. On a 30-year mortgage at 6.5%, you pay 127.5% of the principal in interest. On a 15-year mortgage at the same rate, you pay only 56.8% of the principal in interest. This ratio helps you evaluate whether refinancing, making extra payments, or choosing a shorter term would be financially beneficial.
This calculator handles mortgages, auto loans, personal loans, student loans, and any other fixed-rate amortizing debt. It also supports different payment frequencies — bi-weekly payments effectively add one extra monthly payment per year, which can reduce a 30-year mortgage by 4-5 years and save tens of thousands in interest.
The PMT formula is: PMT = PV × r / (1 - (1 + r)-n)
Each payment has two components: interest on the outstanding balance and principal repayment. Early payments are mostly interest; later payments are mostly principal — this is called amortization.
The Payment Amount is your fixed periodic payment. Total Amount Paid is the payment multiplied by the number of periods — this is the actual cash outflow over the life of the loan. Total Interest Paid is the difference between total payments and the original principal — the true cost of borrowing. The Interest-to-Principal Ratio expresses total interest as a percentage of the loan amount.
Inputs
Results
$300K mortgage at 7% for 30 years: $1,995.91/month, $418,528 total interest
Inputs
Results
$35K auto loan at 5.5% for 5 years: $668.43/month, $5,106 total interest
PMT = PV × r / (1 - (1+r)^-n), where PV is the loan amount, r is the per-period interest rate, and n is the total number of payments. This formula calculates the fixed periodic payment needed to fully repay a loan.
Because interest is calculated on the outstanding balance, and with a 30-year term, the balance remains high for a long time. In the first year of a $300K mortgage at 7%, about $1,750 of each $1,996 monthly payment goes to interest — only $246 reduces the principal.
Bi-weekly payments (every 2 weeks) result in 26 half-payments per year instead of 12 full payments — equivalent to 13 monthly payments. This typically shaves 4-5 years off a 30-year mortgage and saves 20-25% in total interest.
A 15-year mortgage has higher monthly payments but much lower total interest. For a $300K loan at 7%: 30-year costs $418K in interest vs. 15-year costs ~$186K — saving $232K. Choose based on your budget and cash flow needs.
Each 1% increase in rate raises the monthly payment significantly. On a $300K 30-year mortgage: 5% = $1,610/month, 6% = $1,799/month, 7% = $1,996/month, 8% = $2,201/month.
Amortization is the process of paying off a loan through regular equal payments. Early payments are mostly interest; later payments are mostly principal. An amortization schedule shows the breakdown of each payment over the loan's life.
Yes. Enter the car price minus down payment as the loan amount, the annual interest rate, and the loan term. Car loans typically range from 3-7 years with rates from 3-10% depending on credit score and market conditions.
PMT is the single payment amount calculation. An amortization schedule breaks down each PMT payment into its interest and principal components over the entire loan term, showing how the balance decreases over time.
Extra payments go directly to reducing the principal. Paying an extra $100/month on a $300K 30-year mortgage at 7% saves approximately $78,000 in interest and pays off the loan 5 years early.
Yes, by rearranging the formula. If you want to accumulate a future value through regular deposits, use the future value of annuity calculator instead, which solves a slightly different problem.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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