Answer :
To determine the annual income needed if the maximum allowable recurring debt is [tex]$500 under the 28/36 ratio, follow these steps:
1. Understand the 28/36 ratio:
- The 28/36 ratio is a guideline that suggests no more than 36% of your monthly income should go towards all your debt payments, including housing.
2. Identify the maximum allowable debt:
- The problem states that the maximum allowable recurring debt is $[/tex]500.
3. Calculate the monthly income:
- Since 36% of your monthly income is allocated to debt, you can set up the equation:
[tex]\[ 0.36 \times \text{{monthly income}} = 500 \][/tex]
- Solving for the monthly income:
[tex]\[ \text{{monthly income}} = \frac{500}{0.36} \approx 1388.89 \][/tex]
4. Convert the monthly income to annual income:
- Multiply the monthly income by 12 (months in a year) to find the annual income:
[tex]\[ \text{{annual income}} = 1388.89 \times 12 \approx 16666.67 \][/tex]
After determining the annual income, we look for the closest choice provided in the options:
- [tex]\( a. \$21,430 \)[/tex]
- [tex]\( b. \$30,000 \)[/tex]
- [tex]\( c. \$62,500 \)[/tex]
- [tex]\( d. \$75,000 \)[/tex]
Since the calculated annual income is approximately [tex]\( \$16,666.67 \)[/tex], none of the listed choices precisely match. Thus, it appears there might be an error in the provided choices or a misinterpretation of the problem constraints. Based on our calculations, the required annual income to support a [tex]$500 maximum monthly debt under a 36% debt-to-income ratio is closest to approximately $[/tex]16,667, which is different from the options given.
3. Calculate the monthly income:
- Since 36% of your monthly income is allocated to debt, you can set up the equation:
[tex]\[ 0.36 \times \text{{monthly income}} = 500 \][/tex]
- Solving for the monthly income:
[tex]\[ \text{{monthly income}} = \frac{500}{0.36} \approx 1388.89 \][/tex]
4. Convert the monthly income to annual income:
- Multiply the monthly income by 12 (months in a year) to find the annual income:
[tex]\[ \text{{annual income}} = 1388.89 \times 12 \approx 16666.67 \][/tex]
After determining the annual income, we look for the closest choice provided in the options:
- [tex]\( a. \$21,430 \)[/tex]
- [tex]\( b. \$30,000 \)[/tex]
- [tex]\( c. \$62,500 \)[/tex]
- [tex]\( d. \$75,000 \)[/tex]
Since the calculated annual income is approximately [tex]\( \$16,666.67 \)[/tex], none of the listed choices precisely match. Thus, it appears there might be an error in the provided choices or a misinterpretation of the problem constraints. Based on our calculations, the required annual income to support a [tex]$500 maximum monthly debt under a 36% debt-to-income ratio is closest to approximately $[/tex]16,667, which is different from the options given.
