Final answer:
To determine the maximum mortgage you can qualify for with a $50,000 annual income and a mortgage payment limit of 33% of your monthly income,subtract the property taxes and apply the mortgage payment formula. The maximum mortgage you can qualify for is estimated to be $197,403.09.
Step-by-step explanation:
To determine the maximum mortgage you can qualify for, you need to calculate your monthly income after making other debt payments and paying property taxes. In this case, your annual income is $50,000, so your monthly income would be $50,000 / 12 = $4166.67. After subtracting the property taxes of $500, you have $4166.67 - $500 = $3666.67 left for your mortgage payment.
The lender allows your mortgage payment to be no more than 33% of your monthly income, so you can calculate the maximum mortgage payment as $3666.67 * 0.33 = $1211.11.
To find the maximum mortgage you can qualify for, you can use the mortgage payment formula: Mortgage Payment = Loan Amount * Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Months)). In this case, the monthly interest rate is 5% / 12 = 0.4167% and the number of months is 30 * 12 = 360. Plugging in these values, you can solve for the Loan Amount: $1211.11 = Loan Amount * 0.004167 / (1 - (1 + 0.004167)^(-360)). Solving for the Loan Amount, you get: Loan Amount = $1211.11 * (1 - (1 + 0.004167)^(-360)) / 0.004167.
Calculating this expression, you will find that the maximum mortgage you can qualify for is approximately $197,403.09.