Certainly! Let's break down the problem step-by-step:
1. Initial Credit Score of the Consumer:
- The initial credit score of the consumer is given as 670.
2. Decrease in Credit Score:
- The credit score of the consumer decreases by 105 points.
3. Calculating the New Credit Score:
- To get the new credit score, subtract the decrease from the initial credit score:
[tex]\[
\text{New Credit Score} = 670 - 105 = 565
\][/tex]
4. Determining the Interest Rate:
- Based on the new credit score, we need to find the corresponding interest rate:
[tex]\[
\text{New Credit Score} = 565
\][/tex]
- Refer to the given FICO score table:
[tex]\[
\begin{array}{|c|l|}
\hline
\text{FICO Soore} & \text{Simple Interest Rate} \\
\hline
800-850 & 4.295\% \\
\hline
740-799 & 5.597\% \\
\hline
670-739 & 8.132\% \\
\hline
580-669 & 9.358\% \\
\hline
300-579 & 12.413\% \\
\hline
\end{array}
\][/tex]
5. Finding the Interest Rate for Credit Score 565:
- The new credit score 565 falls within the range 300-579.
- According to the table, the interest rate for this range is:
[tex]\[
\text{Interest Rate} = 12.413\%
\][/tex]
6. Conclusion:
- Therefore, after the decrease in their credit score, the consumer will qualify for an interest rate of 12.413%.
So, the correct answer is:
[tex]\[
\boxed{12.413\%}
\][/tex]
