To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to calculate the interest she would pay at both FICO scores and then find the difference between these amounts.
1. Identify the interest rates for both FICO scores:
- For a FICO score of 665, the interest rate is [tex]\(10.358\%\)[/tex].
- For a FICO score of 680, the interest rate is [tex]\(9.132\%\)[/tex].
2. Convert the percentage rates to decimal form:
- Interest rate for 665: [tex]\(10.358\% = 0.10358\)[/tex]
- Interest rate for 680: [tex]\(9.132\% = 0.09132\)[/tex]
3. Calculate the interest amount for each FICO score using the simple interest formula:
The simple interest formula is:
[tex]\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\][/tex]
Assuming Kamryn borrows the money for 1 year, Time ([tex]\(T\)[/tex]) is 1 year.
- For a FICO score of 665:
[tex]\[
\text{Interest}_{665} = 13,250 \times 0.10358 \times 1 = 13,250 \times 0.10358 = 1372.435
\][/tex]
- For a FICO score of 680:
[tex]\[
\text{Interest}_{680} = 13,250 \times 0.09132 \times 1 = 13,250 \times 0.09132 = 1209.99
\][/tex]
4. Calculate the interest saved by improving the FICO score:
[tex]\[
\text{Interest Saved} = \text{Interest}_{665} - \text{Interest}_{680} = 1372.435 - 1209.99 = 162.445
\][/tex]
Thus, the amount of interest Kamryn will save by raising her credit score from 665 to 680 is \[tex]$162.45. The correct answer is:
c) \$[/tex]162.45
