Questions: 1. You are buying a home for 400,000 with a 10% down payment. The annual interest rate is 6% and the mortgage term is 20 years calculate the monthly mortgage payment Questions 2: create a monthly budget that Includes the mortgage payment, property taxes ( 4,800 annually ), utilities and other personal expenses.Ensure that the total expenses do not go over 3,500 per month

## Step 1: Calculate the Loan Amount<br />### The down payment is $10\%$ of $\$400,000$, which is $0.10 \times \$400,000 = \$40,000$. Subtracting this from the home price gives the loan amount: $\$400,000 - \$40,000 = \$360,000$.<br /><br />## Step 2: Calculate the Monthly Interest Rate<br />### The annual interest rate is $6\%$. To find the monthly rate, divide by 12: $\frac{6\%}{12} = \frac{0.06}{12} = 0.005$.<br /><br />## Step 3: Calculate the Number of Payments<br />### The mortgage term is 20 years. Since there are 12 months in a year, the total number of payments is $20 \times 12 = 240$.<br /><br />## Step 4: Calculate the Monthly Mortgage Payment<br />### Using the formula for monthly mortgage payment: $M = P \frac{r(1+r)^n}{(1+r)^n - 1}$, where $M$ is the monthly payment, $P$ is the loan amount, $r$ is the monthly interest rate, and $n$ is the number of payments.<br />$M = \$360,000 \times \frac{0.005(1+0.005)^{240}}{(1+0.005)^{240} - 1}$<br />$M = \$360,000 \times \frac{0.005(1.005)^{240}}{(1.005)^{240} - 1}$<br />$M = \$360,000 \times \frac{0.005 \times 3.3102}{3.3102 - 1}$<br />$M = \$360,000 \times \frac{0.016551}{2.3102}$<br />$M = \$360,000 \times 0.007164$<br />$M \approx \$2,579.04$<br /><br />## Step 5: Create a Monthly Budget<br />### Given a monthly mortgage payment of approximately $\$2,579.04$, annual property taxes of $\$4,800$, and a total monthly expense limit of $\$3,500$, we can create a budget. Monthly property taxes are $\frac{\$4,800}{12} = \$400$. This leaves $\$3,500 - \$2,579.04 - \$400 = \$520.96$ for utilities and other personal expenses.