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Based on a [tex]$\$[/tex]400[tex]$ loan amount, rank the following companies from the lowest to highest annual percentage rate (APR).

\begin{tabular}{|c|c|c|}
\hline
Company & Fees Charged & Term of Loan \\
\hline
A & $[/tex]\[tex]$40$[/tex] & 5 days \\
\hline
B & [tex]$\$[/tex]50[tex]$ & 12 days \\
\hline
C & $[/tex]\[tex]$80$[/tex] & 15 days \\
\hline
D & [tex]$\$[/tex]100[tex]$ & 20 days \\
\hline
\end{tabular}

a. $[/tex]A, B, C, D[tex]$
b. $[/tex]B, D, C, A[tex]$
c. $[/tex]D, B, C, A[tex]$
d. $[/tex]D, C, B, A$

Please select the best answer from the choices provided.



Answer :

GinnyAnswer
To determine the ranking of the companies from the lowest to the highest annual percentage rate (APR) based on a \[tex]$400 loan amount, we need to calculate the APR for each company using the given fees and loan terms. Here are the details again for reference: - Company A: \$[/tex]40 fee for 5 days
- Company B: \[tex]$50 fee for 12 days - Company C: \$[/tex]80 fee for 15 days
- Company D: \$100 fee for 20 days

The formula to calculate the APR is given by:
[tex]\[ \text{APR} = \left( \frac{\text{fee}}{\text{loan amount}} \right) \times \left( \frac{365}{\text{term in days}} \right) \times 100 \][/tex]

Let's calculate the APR for each company step-by-step:

1. Company A:
[tex]\[ \text{APR}_A = \left( \frac{40}{400} \right) \times \left( \frac{365}{5} \right) \times 100 = 0.1 \times 73 \times 100 = 730.00\% \][/tex]

2. Company B:
[tex]\[ \text{APR}_B = \left( \frac{50}{400} \right) \times \left( \frac{365}{12} \right) \times 100 = 0.125 \times 30.4167 \times 100 = 380.21\% \][/tex]

3. Company C:
[tex]\[ \text{APR}_C = \left( \frac{80}{400} \right) \times \left( \frac{365}{15} \right) \times 100 = 0.2 \times 24.3333 \times 100 = 486.67\% \][/tex]

4. Company D:
[tex]\[ \text{APR}_D = \left( \frac{100}{400} \right) \times \left( \frac{365}{20} \right) \times 100 = 0.25 \times 18.25 \times 100 = 456.25\% \][/tex]

Having calculated the APRs, we get:
- APR of Company A: [tex]\( 730.00\%\)[/tex]
- APR of Company B: [tex]\( 380.21\%\)[/tex]
- APR of Company C: [tex]\( 486.67\%\)[/tex]
- APR of Company D: [tex]\( 456.25\%\)[/tex]

Now, let's rank the companies from the lowest to the highest APR:
1. Company B: [tex]\(380.21\%\)[/tex]
2. Company D: [tex]\(456.25\%\)[/tex]
3. Company C: [tex]\(486.67\%\)[/tex]
4. Company A: [tex]\(730.00\%\)[/tex]

Thus, the correct order is Company B, Company D, Company C, and Company A.

So, the best answer is:
[tex]\[ \text{c. } D, B, C, A \][/tex]

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