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Carl Sonntag wanted to compare the proceeds he would receive with a simple interest note versus a simple discount note. Both had the same terms: [tex][tex]$\$[/tex]17,125[tex]$[/tex] at [tex]9\%[/tex] for 4 years. Use ordinary interest as needed.

a. Calculate the simple interest note proceeds.

b. Calculate the simple discount note proceeds.

\begin{tabular}{l|l}
\hline Simple discount note proceeds $[/tex]\quad \[tex]$ \quad 10,960$[/tex] \\
\hline
\end{tabular}


Sagot :

Sure, I'll walk you through the calculations for both parts step-by-step.

### Part (a): Calculate the simple interest note proceeds

To determine the simple interest note proceeds, we follow these steps:

1. Find the Simple Interest:
[tex]\[ \text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Given:
- Principal (P) = \[tex]$17,125 - Rate (R) = 9% (or 0.09 in decimal form) - Time (T) = 4 years Plugging in the values, we get: \[ \text{Simple Interest} = 17125 \times 0.09 \times 4 = \$[/tex]6165.00
\]

2. Calculate the Note Proceeds:
[tex]\[ \text{Simple Interest Note Proceeds} = \text{Principal} + \text{Simple Interest} \][/tex]
Given the simple interest we just calculated:
[tex]\[ \text{Simple Interest Note Proceeds} = 17125 + 6165 = \$23,290.00 \][/tex]

So, the simple interest note proceeds amount to \[tex]$23,290.00. ### Part (b): Calculate the simple discount note proceeds For this part, we use the given value for the simple discount note proceeds directly. From the information provided: \[ \text{Simple Discount Note Proceeds} = \$[/tex]10,960.00
\]

### Summary

Let's neatly summarize the two parts:

- Simple Interest Note Proceeds: \[tex]$23,290.00 - Simple Discount Note Proceeds: \$[/tex]10,960.00
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