calculate-loan

01 Loan payments

15-Year Mortgage Calculator: Payment and Total Interest

Calculator No. 01-6684 · Updated · Formula and assumptions shown below

The calculator on this page is switched off while it is checked. The formula is below, and the worked example shows how to do the sum by hand.

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

This 15-year mortgage calculator estimates the monthly principal-and-interest payment and total interest for a fixed-rate loan. Enter the amount borrowed and the APR; the result uses a 15-year term, or 180 monthly payments, to show how the numbers work.

Formula

The calculator applies the standard fixed-payment loan formula. It converts the annual percentage rate to a monthly rate, calculates a level payment across all monthly installments, rounds that payment to cents, then uses the rounded payment to estimate total payments and interest.

Monthly payment: M = round(P × r / [1 − (1 + r)−n], 2). Total payments: T = M × n. Total interest: I = T − P.

  • P is the starting mortgage principal in dollars.
  • APR is the annual percentage rate entered as a percentage; the monthly rate r = APR / 1200.
  • y is the term in years, and n = 12 × y is the number of monthly payments.
  • M is the estimated monthly principal-and-interest payment in dollars.
  • T is the sum of the scheduled payments; I is their amount above the starting principal.

A 15-year term means 180 payments when payments are monthly and the term is exactly 15 years. The term field is included so the same calculation can illustrate a different duration; for a 15-year estimate, leave it at 15.

Worked Example

Using the calculator’s defaults: principal P = $300,000, APR = 6.5%, and term y = 15 years.

  1. Convert APR to a monthly rate: r = 6.5 / 1200 = 0.0054166667.
  2. Calculate the number of payments: n = 15 × 12 = 180.
  3. Apply the payment formula: M = round[300,000 × 0.0054166667 / (1 − (1.0054166667)−180), 2] = $2,613.28 per month.
  4. Multiply the rounded payment by 180: T = $2,613.28 × 180 = $470,390.40.
  5. Subtract principal: I = $470,390.40 − $300,000 = $170,390.40 in estimated interest.

Assumptions

  • The interest rate is fixed for the full modeled term.
  • Payments are equal, made monthly at the end of each period; the calculation uses monthly compounding at APR / 12.
  • The payment is rounded to cents, and total interest is calculated from that rounded payment. A real final installment may be adjusted for lender rounding or payment processing.
  • Principal-and-interest only: fees, taxes, homeowners insurance, mortgage insurance (PMI), escrow, and any additional payments are not included.

What a 15-Year Mortgage Estimate Shows

A 15-year mortgage is a home loan scheduled to be repaid through monthly payments over 15 years. The calculator isolates the basic amortizing loan arithmetic: the amount borrowed, interest rate, and repayment period. It does not determine an actual offer or quote; use the APR and loan amount supplied for the scenario you want to estimate.

The monthly payment is not the same as a complete housing payment. Property-related taxes, homeowners insurance, mortgage insurance, association dues, and other charges may be collected separately or included in a monthly bill. Because none of these costs is entered here, do not treat the displayed principal-and-interest figure as a full estimate of monthly housing expenses.

How to Read the Results

The first result is the modeled monthly principal-and-interest payment. “Total of payments” multiplies that amount by the number of scheduled installments, while “total interest” subtracts the original principal from that sum. These totals assume every payment is made as scheduled and no extra principal is paid.

For the example, the $170,390.40 interest result is not a separate charge due immediately; it is the modeled sum of interest over the full schedule. As principal is repaid, the interest portion of each level payment generally declines and the principal portion rises. The figures are estimates rather than a lender’s payment schedule.

Common Mistakes and Limits

One common error is entering an APR as a decimal: enter 6.5 for 6.5%, not 0.065. Another is confusing the original purchase price with the loan principal; the amount borrowed can differ from the home price. Check that the APR and principal refer to the same loan scenario, and remember that changing the term changes both the payment count and calculated totals.

The formula assumes a constant rate and equal monthly payments. It does not model adjustable rates, irregular payment dates, closing costs, prepaid interest, late payments, skipped payments, or extra principal. A real loan may also use detailed daily calculations and a final payment that differs slightly because of rounding. To include other costs, obtain their amounts separately and add them to the principal-and-interest estimate only when appropriate.

Use this calculation to understand the basic relationship between principal, APR, and term, not to decide whether to take, decline, or refinance a loan. Rates and fees are inputs, not predictions; obtain the actual figures and schedule from the lender. The result is an estimate, and the lender’s disclosure gives the exact figures.

Frequently Asked Questions

How many payments are in a 15-year mortgage?
With monthly payments and an exact 15-year term, there are 180 scheduled payments.

Does the monthly result include property taxes and insurance?
No. It estimates principal and interest only; taxes, insurance, mortgage insurance, and escrow are outside the calculation.

Why can the final payment differ from this estimate?
Lender schedules can reflect rounding, payment dates, accrued interest, or other loan-specific details that this standard formula does not model.

Can I enter a different mortgage term?
Yes. Change the term input to calculate a different duration; for a 15-year mortgage estimate, use 15 years.

Does the calculator account for extra payments?
No. It assumes only the scheduled equal monthly payment, so extra principal payments and their effect on payoff timing are not included.

Final Thoughts

A 15-year mortgage estimate translates a loan amount, APR, and term into a scheduled payment and approximate lifetime interest. Check the inputs carefully, account separately for excluded housing costs, and use lender-provided disclosures for the exact loan figures.

Related

Formula used
in p | Mortgage amount | $ | 300000 | 1 | 100000000
in apr | Interest rate (APR) | % | 6.5 | 0.01 | 100
in yrs | Loan term | years | 15 | 0.0833 | 50
out pmt | Monthly principal-and-interest payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2
out tot | Total of payments | $ | pmt * yrs * 12 | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

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