Question 6 of 15, Step 1 of 1 Manuel purchases a house and gets a 30 -year mortgage for \( \$ 140,000 \) at \( 4.75 \% \) APR. In addition to the monthly payment, the lender requires him to pay into an escrow account for the homeowners insurance and property tax. His homeowners insurance is \( \$ 1000 \) per year and the property tax is \( \$ 1400 \) per year, Determine the monthly payment to the lender that includes the insurance and property tax. Round your answer to the nearest cent. Formulas \( \begin{array}{l}\text { Regular Payment for Fixed } \\ \text { Installment Loans } \\ \text { Number of Fixed Payments } \\ \text { Required to Pay Off Credit Card } \\ \text { Debt }\end{array} \quad \mathrm{R}=\frac{-\log \left[1-\frac{\mathrm{r}}{\mathrm{n}}\left(\frac{\mathrm{A}}{\mathrm{PMT}}\right)\right]}{\log \left(1+\frac{\mathrm{r}}{\mathrm{n}}\right)} \) Answer

To calculate the monthly mortgage payment, you first need to determine the regular monthly payment for the loan amount. Using the formula for monthly mortgage payments (PMT) and plugging in the loan amount of \( \$140,000 \), an interest rate of \( \frac{4.75}{12} = 0.3958\% \), and a period of \( 30 \times 12 = 360 \) months, the monthly payment will be approximately \( \$730.61 \). Next, add the monthly amounts for homeowners insurance and property tax. The insurance costs \( \frac{1000}{12} = \$83.33 \) and property tax \( \frac{1400}{12} = \$116.67 \). Combining these, the total monthly payment including insurance and tax is approximately \( \$730.61 + \$83.33 + \$116.67 = \$930.61 \). So, the final answer rounded to the nearest cent is \( \$930.61 \). For some historical flair, did you know that the concept of mortgages dates back to ancient Rome? In those days, lenders would give money to people purchasing land, and if the borrower failed to repay, the lender could take possession of the property, much like today! As for real-world applications, understanding how escrow accounts work is crucial. They provide peace of mind by ensuring your property taxes and insurance are paid on time, preventing potential pitfalls of late fees or lapses in coverage that can lead to bigger financial headaches down the road!