Let's break down the problem step-by-step to understand how many points Mariah needs to improve her credit score to afford a mortgage for [tex]$150,000 given her annual payment budget of $[/tex]12,500.
1. Calculate Monthly Payment Budget:
- Mariah can afford to pay [tex]$12,500 per year.
- Monthly payment budget:
\[
\frac{12,500}{12} \approx 1041.67
\]
2. Analyze Current Credit Score:
- Mariah's current credit score is 531.
- According to the table, a score of 531 falls in the $[/tex]500-559[tex]$ range, with a monthly payment of $[/tex]1,238.
3. Compare Current Monthly Payment with Budget:
- The monthly payment of [tex]$1,238 exceeds her budget of $[/tex]1,041.67.
4. Determine Required Credit Score Improvement:
- We need to determine the credit score range where the monthly payment is within her budget.
- Looking at the table, the [tex]$560-619$[/tex] range has a monthly payment of [tex]$1,157, which is still above her budget.
- Next, we look at the $[/tex]620-674[tex]$ range, where the monthly payment is $[/tex]1,038, which is within her budget ([tex]$1,038 < $[/tex]1,041.67).
5. Calculate Points Needed to Reach Affordable Score Range:
- To move from her current score (531) to the next acceptable range ($620-674), she needs to reach at least a score of 620.
- Therefore,
[tex]\[
620 - 531 = 89
\][/tex]
Hence, Mariah needs to improve her credit score by 89 points.
So, the answer is:
D. 89 points
