To determine the ranking of the companies from the lowest to highest annual percentage rate (APR), let’s analyze the given data for each company.
The APR can be calculated using the formula:
[tex]\[
\text{APR} = \left(\frac{\text{Fees Charged}}{\text{Loan Amount}}\right) \times \left(\frac{365}{\text{Term of Loan in Days}}\right) \times 100
\][/tex]
Given:
- Loan Amount = \[tex]$400
Let’s calculate the APR for each company:
Company A:
- Fees Charged = \$[/tex]40
- Term of Loan = 5 days
[tex]\[
\text{APR}_A = \left(\frac{40}{400}\right) \times \left(\frac{365}{5}\right) \times 100
\][/tex]
[tex]\[
\text{APR}_A = 0.1 \times 73 \times 100 = 730\%
\][/tex]
Company B:
- Fees Charged = \[tex]$50
- Term of Loan = 12 days
\[
\text{APR}_B = \left(\frac{50}{400}\right) \times \left(\frac{365}{12}\right) \times 100
\]
\[
\text{APR}_B = 0.125 \times 30.4167 \times 100 = 380.20\%
\]
Company C:
- Fees Charged = \$[/tex]80
- Term of Loan = 15 days
[tex]\[
\text{APR}_C = \left(\frac{80}{400}\right) \times \left(\frac{365}{15}\right) \times 100
\][/tex]
[tex]\[
\text{APR}_C = 0.2 \times 24.3333 \times 100 = 486.67\%
\][/tex]
Company D:
- Fees Charged = \$100
- Term of Loan = 20 days
[tex]\[
\text{APR}_D = \left(\frac{100}{400}\right) \times \left(\frac{365}{20}\right) \times 100
\][/tex]
[tex]\[
\text{APR}_D = 0.25 \times 18.25 \times 100 = 456.25\%
\][/tex]
Now, let’s rank the companies from the lowest to the highest APR:
- APR_B = 380.20%
- APR_D = 456.25%
- APR_C = 486.67%
- APR_A = 730%
So, the ranking is:
[tex]\[ \text{B, D, C, A} \][/tex]
Therefore, the answer is:
b. B, D, C, A
