Solution
- The formulas needed to solve the question are:
[tex]\begin{gathered} \text{ Let discount be D} \\ \text{ Let proceeds be P} \\ \text{ Let effective rate be E} \\ \text{ Let M be face value} \\ r\text{ be the rate} \\ t\text{ be the time in years} \\ \\ D=M\times r\times t \\ \\ P=M-D \\ \\ E=\frac{D}{P}\times100\% \end{gathered}[/tex]- Thus, we can solve the questions as follows:
Question 1:
[tex]\begin{gathered} Bank\text{ }Discount(D): \\ D=Mrt \\ D=12000\times\frac{7}{100}\times\frac{180}{360}\text{ \lparen360 days corresponds to 1 commercial year\rparen} \\ \\ D=\$420 \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} Proceeds(P): \\ P=M-D \\ P=12000-420 \\ P=\$11,580 \end{gathered}[/tex]Question 3:
[tex]\begin{gathered} E=\frac{D}{P}\times100\% \\ \\ E=\frac{420}{11,580}\times100\% \\ \\ E=3.62694...\approx3.627 \end{gathered}[/tex]