Questions: Use the banker's rule. Find the maturity value of the undiscounted promissory note shown The maturity value of the undiscounted promissory note is . (Round to the nearest cent as needed.)

Solution Steps

To find the maturity value of an undiscounted promissory note using the banker's rule, we need to determine the time period between the issue date and the maturity date in terms of days. This can be done using the sequential numbers for dates of the year. Once the time period is determined, we can calculate the maturity value using the formula for simple interest: \( \text{Maturity Value} = \text{Principal} + \text{Principal} \times \text{Rate} \times \text{Time} \). The rate is typically given as an annual rate, so the time should be in years.

To find the maturity value of the promissory note, we first need to determine the time period between the issue date and the maturity date. The issue date is January 16, and the maturity date is April 16. Using the sequential numbers for dates of the year, January 16 corresponds to day 16, and April 16 corresponds to day 106. Therefore, the time period in days is:

\[ \text{Time Period} = 106 - 16 = 90 \text{ days} \]

The banker's rule assumes a year has 360 days. Therefore, we convert the time period from days to years:

\[ \text{Time Period in Years} = \frac{90}{360} = \frac{1}{4} \text{ years} \]

The maturity value is calculated using the formula for simple interest:

\[ \text{Maturity Value} = \text{Principal} + \text{Principal} \times \text{Rate} \times \text{Time} \]

Given:

• Principal = \$1000
• Annual Rate = 0.05
• Time = \(\frac{1}{4}\) years

Substitute these values into the formula:

\[ \text{Maturity Value} = 1000 + 1000 \times 0.05 \times \frac{1}{4} \]

\[ = 1000 + 12.5 = 1012.5 \]

Final Answer