Assume you have found a home for sale and agreed on a purchase price of \( \$ 290,600 \). Down Payment and Loan You will make a \( 10 \% \) down payment on the house. Calculate the following: Down Payment: \$ \( \square \) 29,060 Loan Amount: \$ \( \square \) 261540 Monthly Payment Calculate the monthly payment for a 30-year loan, rounding your final answer to the nearest cent (two decimal places). Use the following details: Annual Interest Rate: 7.5\% Express the annual interest rate as a decimal: 0.075 Use the loan formula to calculate the monthly payment: \[ \mathrm{P}_{0}=\frac{d\left(1-\left(1+\frac{r}{n}\right)^{-n t}\right)}{\left(\frac{r}{n}\right)} \] - \( P_{0} \) : Loan amount - \( r \) : Annual interest rate (decimal) - \( n \) : Compounding periods per year \( (\mathrm{n}=12) \) - \( t \) : Loan term in years \( (\mathrm{t}=30) \) Monthly Payment: \$ 1.828 .73
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The Deep Dive
Did you know that the concept of mortgage payments has been around for centuries? In fact, contracts similar to modern mortgages can be traced back to ancient Egypt, where land transactions involved interest payments. Fast forward a few thousand years, and the structure of mortgages has evolved, making homeownership more accessible while also fostering an entire industry focused on lending. When it comes to real-world applications, understanding your monthly mortgage payment is crucial for budgeting. It’s not just about the principal and interest; don’t forget to factor in property taxes, homeowners insurance, and possibly private mortgage insurance (PMI) if your down payment is less than 20%. Knowing the total cost allows you to plan your finances better and helps avoid unexpected monetary pitfalls!