Let's consider the information provided:
1. The homeowner has an initial FICO score of 725.
2. The homeowner plans to raise their FICO score by 40 points.
Step-by-Step Solution:
1. Initial FICO score: [tex]\(725\)[/tex]
2. Increase in FICO score: [tex]\(40\)[/tex] points
3. New FICO score:
[tex]\[
725 (initial \text{ score}) + 40 (\text{increase}) = 765
\][/tex]
4. Determine the applicable interest rate for a FICO score of 765:
According to the interest rates based on FICO score ranges:
- [tex]\(800-850\)[/tex]: [tex]\(4.295\% \)[/tex]
- [tex]\(740-799\)[/tex]: [tex]\(5.597\% \)[/tex]
- [tex]\(670-739\)[/tex]: [tex]\(8.132\% \)[/tex]
- [tex]\(580-669\)[/tex]: [tex]\(9.358\% \)[/tex]
- [tex]\(300-579\)[/tex]: [tex]\(12.413\% \)[/tex]
5. A FICO score of 765 falls within the range [tex]\(740-799\)[/tex].
Therefore, the interest rate the homeowner will qualify for after raising their credit score to 765 is [tex]\(5.597\%\)[/tex].
So, the correct answer is:
[tex]\[
5.597\%
\][/tex]
