Use PMT \( =\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} \) to determine the regular payment amount, rounded to the nearest dollar. The price of a home is \( \$ 183,000 \). The bank requires a \( 20 \% \) down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at \( 10 \% \). Complete parts (a) through (e) below. a. Find the required down payment. \( \$ 36,600 \) b. Find the amount of the mortgage. \( \$ 146,400 \) c. How much must be paid for the three points at closing? \( \$ 4,392 \) (Round to the nearest dollar as needed.) d. Find the monthly payment (excluding escrowed taxes and insurance). \( \$ \square \) (Round to the nearest dollar as needed.)

To calculate the monthly payment using the PMT formula, we'll plug in the numbers based on the information provided. First, let's summarize what we have: - Home price: \( P = 183,000 \) - Down payment (20%): \( 36,600 \) - Amount financed (mortgage): \( 146,400 \) - Annual interest rate (r): \( 10\% = 0.10 \) - Number of payments per year (n): \( 12 \) (monthly payments) - Total number of payments (n * t): \( 30 \times 12 = 360 \) Now, substituting these values into the PMT formula: \[ PMT = \frac{146400\left(\frac{0.10}{12}\right)}{\left[1-\left(1+\frac{0.10}{12}\right)^{-360}\right]} \] Calculating the values step-by-step: 1. Calculate \( \frac{r}{n} = \frac{0.10}{12} \approx 0.0083333 \). 2. Calculate \( 1 + \frac{r}{n} = 1 + 0.0083333 \approx 1.0083333 \). 3. Calculate \( (1 + \frac{r}{n})^{-360} \approx (1.0083333)^{-360} \approx 0.0351362 \). 4. Calculate \( 1 - (1 + \frac{r}{n})^{-360} \approx 1 - 0.0351362 \approx 0.9648638 \). 5. Finally, calculate PMT: \[ PMT = \frac{146400 \times 0.0083333}{0.9648638} \approx \frac{1219.83}{0.9648638} \approx 1264.68. \] Rounded to the nearest dollar, your monthly payment is \( \boxed{1265} \). Now let's sneak in that additional knowledge! When it comes to mortgages, understanding the impact of interest rates over the loan term is crucial. Even a small increase in the interest rate can lead to substantially higher monthly payments. It's a classic example of how even a little can go a long way - just like that time you accidentally added an extra zero to your shopping budget! To become a mortgage pro, consider diving into financial literacy resources! Websites like Investopedia and books by financial experts can arm you with the knowledge you need to make informed decisions about your financial future—and maybe even become that friend who always has the best money advice!