A mortgage calculator is a financial tool used to estimate the monthly mortgage payments for a home loan based on various factors such as the loan amount, interest rate, loan term, and sometimes additional fees like property taxes and insurance. It helps potential homebuyers or homeowners understand their potential monthly payments and how changes in loan can affect their financial obligations.
The key components of a mortgage calculator along with the formulas used:
- Loan Amount (Principal) - This is the total amount of money borrowed to purchase a home. It's typically the purchase price minus the down payment.
- Interest Rate - is the annual cost of borrowing money from the lender, expressed as a percentage of the loan amount. It's crucial to know the interest rate, as it significantly affects the monthly mortgage payment.
- Loan Term - The loan term refers to the length of time over which the loan will be repaid. Common loan terms for mortgages are 15, 20 or 30 years.
- Monthly Mortgage Payment - this is the amount the borrower will pay each month to the lender, covering both principal and interest portions of the loan. In addition to the principal and interest, the monthly payment may also include property taxes, homeowner's insurance, and private mortgage insurance (PMI) if applicable.
Monthly Mortgage Payment (PMT)
To calculate the monthly mortgage payment (PMT) you need the know the principal loan amount \(P\), the monthly interest rate (\(r\)), and the total number of payments. The monthly interest rate is the annual interest rate divided by 12. The total number of payments or loan term in years multiplied by 12. The formula for calculating the PMT can be written as:
\begin{equation}
PMT = P\frac{r(1+r)^n}{(1+r)^n - 1}
\end{equation}
where:
- \(PMT\) is the monthly mortgage payment
- \(P\) is the principal loan amount
- \(r\) is the monthly interest rate (annual interest rate divided by 12).
- \(n\) is the total number of payments (loan term in years multiplied by 12).
Monthly Interest Payment (IP)
The monthly interest payment is the portion of the monthly mortgage payment that goes toward paying the interest on the loan for that month. The formula for calculating the IP can be written as:
\begin{equation}
IP = Pr,
\end{equation}
where:
- \(IP\) is the monthly interest payment
- \(P\) is the principal loan amount
- \(r\) is the monthly interest rate (annual interest rate divided by 12).
Monthly Principal Payment (PP)
The monthly principal Payment is the portion of the monthly mortgage payment that goes toward paying down the loan balance (excluding interest). The \(PP\) can be calculated as the difference between monthly payment (PMT) and the monthly interest payment (IP). The equation for calculating PP can be written as:
\begin{equation}
PP = PMT - IP
\end{equation}
where:
- \(PP\) is the monthly principal payment
- \(PMT\) is the monthly mortgage payment
- \(IP\) is the monthly interest payment