Let's break down the problem step-by-step to understand how we arrive at the answer:
1. Understand the Given Information:
- Annual gross income: [tex]$509,750
- Monthly mortgage payment: $[/tex]1,300
- Monthly other expenses: [tex]$1,360
2. Convert Annual Income to Monthly Income:
- To do this, we divide the annual gross income by 12 (since there are 12 months in a year).
- \( \text{Monthly income} = \frac{\$[/tex]509,750}{12} \)
3. Calculate Monthly Income:
- [tex]\( \text{Monthly income} = \$42,479.17 \)[/tex]
4. Calculate the Front-End Ratio:
- The front-end ratio is calculated by dividing the monthly mortgage payment by the monthly income, and then multiplying by 100 to convert it to a percentage.
- [tex]\( \text{Front-End Ratio} = \left( \frac{\$1,300}{\$42,479.17} \right) \times 100 \)[/tex]
5. Calculate the Total Debt Ratio (Back-End Ratio):
- The total debt ratio includes both the monthly mortgage payment and the monthly other expenses.
- [tex]\( \text{Total Debt Ratio} = \left( \frac{\$1,300 + \$1,360}{\$42,479.17} \right) \times 100 \)[/tex]
- Simplify this to [tex]\( \text{Total Debt Ratio} = \left( \frac{\$2,660}{\$42,479.17} \right) \times 100 \)[/tex]
6. Simplify the Calculations:
- After performing these calculations, you will get the Front-End Ratio and Total Debt Ratio to the nearest whole number percentages.
Thus, the answers are:
- Front-End Ratio: 3%
- Total Debt Ratio: 6%
Based on your provided choices and calculations:
- The correct answer for the front-end ratio to the nearest percentage is:
A. 3
Feel free to ask any clarification questions if needed!
