To determine how many points come from the payment history and credit mix categories for a borrower with a credit score of 675, we need to break down the steps:
1. Identify the percentages for each category:
- Payment History: 35%
- Credit Mix: 10%
2. Convert these percentages to decimal form to facilitate calculations:
- Payment History: [tex]\( 35\% = 0.35 \)[/tex]
- Credit Mix: [tex]\( 10\% = 0.10 \)[/tex]
3. Calculate the points from Payment History:
The formula to calculate points from a category is:
[tex]\[
\text{Points from category} = \text{credit score} \times \text{category percentage}
\][/tex]
Applying this to the Payment History category:
[tex]\[
\text{Payment History Points} = 675 \times 0.35 = 236.25
\][/tex]
4. Calculate the points from Credit Mix:
Using the same formula:
[tex]\[
\text{Credit Mix Points} = 675 \times 0.10 = 67.5
\][/tex]
5. Combine the results:
From the calculations:
- Points from Payment History: 236.25
- Points from Credit Mix: 67.5
So, the total points from both categories are:
- Payment History Points: 236.25
- Credit Mix Points: 67.5
The answer choices provided don't ask for a total sum but rather seem to test understanding of components; the correct breakdowns align with the choices offered.
Thus, the points derived from payment history and credit mix for a borrower with a credit score of 675 are [tex]\(236.25\)[/tex] and [tex]\(67.5\)[/tex] respectively.
