Chapter 11, Problem 1ECP

(a)

To determine

The bank’s discount of simple discount note of $ 4,250, 190 days at $2\frac{1}{2}\%$ discount rate. Using ordinary interest method.

Answer to Problem 1ECP

The Bank’s discount is $\underset{\_}{\$56.07}$.

Explanation of Solution

Formula used:

$\begin{array}{l}\text{Maturity value}=\text{Face value}\left(\text{principal}\right)+\text{Interest}\\ \text{Bank discount}=\text{Maturity value}\times \text{Bank discount rate}\times \text{Time}\end{array}$

Calculation:

Given that, $\text{Face}\text{value}=\$4,250$.

Now, substitute $\text{Face}\text{value}=\$4,250$ in first equation.

$\text{Maturity value}=\text{Face value}\left(\text{principal}\right)+\text{Interest}$

For non-interest-bearing promissory note, the equation becomes,

$\begin{array}{c}\text{Maturity value}=\text{Face value}\\ =\$4,250\end{array}$

Hence, the maturity value is $\$4,250$.

Substitute, $\text{Maturity value}=\text{\$4,250, Bank discount rate}=2\frac{1}{2}\text{\%,}$ and $\text{Time}=190\text{ days}$ in second equation.

$\begin{array}{c}\text{Bank discount}=\text{Maturity value}\times \text{Bank discount rate}\times \text{Time}\\ =4,250\times \frac{2.5}{100}\times \frac{190}{360}\\ =4,250\times 0.025\times 0.5278\\ =56.07\end{array}$

Hence, the Bank’s discount is $\underset{\_}{\$56.07}$.

(b)

To determine

The proceeds of simple discount note of $ 4,250, 190 days at $2\frac{1}{2}\%$ discount rate. Using ordinary interest method.

Answer to Problem 1ECP

The proceeds is $\underset{\_}{\$4,193.93}$.

Explanation of Solution

Formula used:

$\text{Proceeds}=\text{Maturity value}-\text{Bank discount}$

Calculation:

From part (a) the Maturity value is $4,250 and Bank discount is $56.07.

Substitute $\text{Maturity}\text{value}=\$4,250,\text{Bank discount}=\$56.07$ in the above mentioned formula.

$\begin{array}{c}\text{Proceeds}=\text{Maturity value}-\text{Bank discount}\\ =4,250-56.07\\ =4,193.93\end{array}$

Hence, the Proceeds is $\underset{\_}{\$4,193.93}$.