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Mortgage Calculator

Mortgage Calculator

Answer:
Monthly Payment: $ 848.14

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Step-by-Step
Mortgage Payment Calculation

Using the mortgage payment formula:

\( PMT=\dfrac{PVi(1+i)^n}{(1+i)^n-1} \)
Present Value of the Mortgage (PV):
PV = 175,000

Monthly interest rate as a decimal:
i = Interest Rate / 100 / 12
i = 4.125% / 100 / 12
i = 0.003438

Number of monthly payments:
n = years × 12
n = 30 × 12
n = 360

\( PMT=\dfrac{PVi(1+i)^n}{(1+i)^n-1} \)
\( = \dfrac{175,000 \times 0.003438(1+0.003438)^{360}}{(1+0.003438)^{360}-1} \)
\( = \dfrac{175,000 \times 0.003438(1.003438)^{360}}{(1.003438)^{360}-1} \)
\( = \dfrac{175,000 \times 0.003438 \times 3.4397}{3.4397-1} \)
\( PMT = \dfrac{2,069.181393}{2.439678} \)
\( PMT = 848.14 \)

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Calculator Use

Calculate your monthly mortgage payments on your home based on term of your mortgage, interest rate, and mortgage loan amount. To include annual insurance and taxes in your calculations, use this mortgage calculator with taxes and insurance.

Mortgage Amount
the original principal amount of your mortgage when calculating a new mortgage or the current principal owed when calculating a current mortgage
Mortgage Term
the original term of your mortgage or the time left when calculating a current mortgage
Interest Rate
the annual nominal interest rate or stated rate on the loan. Note that this is the interest rate you are being charged which is different and normally lower than the Annual Percentage Rate (APR).
Monthly Payment
the payment amount to be paid on this mortgage on a monthly basis toward principal and interest only.  This does not include insurance or taxes or escrow payments. (payment = principal + interest)

Monthly Payment Calculation

Monthly mortgage payments are calculated using the following formula:

\( PMT=\dfrac{PVi(1+i)^n}{(1+i)^n-1} \)

where n = is the term in number of months, PMT = monthly payment, i = monthly interest rate as a decimal (interest rate per year divided by 100 divided by 12), and PV = mortgage amount (present value).

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This article provides authoritative insights around Financial topics and calculations, and provides a free Mortgage Calculator tool.
Key entities: CalculatorSoup.com + Calculators + Financial Calculators + Loans Calculators
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Cite this content, page or calculator as:

Furey, Edward "Mortgage Calculator" at https://www.calculatorsoup.com/calculators/financial/mortgage-calculator.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: August 1, 2025

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