Sure, let's work through this problem step-by-step.
1. Identify the given values:
- Principal (P): $700.00
- Interest Rate (R): 15% per year (which is 0.15 as a decimal)
- Term (T): 90 days
2. Convert the term to a fraction of a year:
- There are typically 360 days considered in a financial year for these purposes (ordinary interest method).
- So, the fraction of the year for 90 days is \( \frac{90}{360} \).
3. Calculate the interest using the ordinary interest formula:
The ordinary interest formula is \( I = P \times R \times T \).
Substituting in the values we have:
[tex]\[
I = 700 \times 0.15 \times \frac{90}{360}
\][/tex]
Simplifying the fraction \( \frac{90}{360} \) to \( \frac{1}{4} \) or 0.25:
[tex]\[
I = 700 \times 0.15 \times 0.25
\][/tex]
Finally:
[tex]\[
I = 700 \times 0.0375 = 26.25
\][/tex]
4. Calculate the total payment required:
- The total payment is the principal plus the interest: \( P + I \)
Substituting the values we have:
[tex]\[
\text{Total Payment} = 700 + 26.25 = 726.25
\][/tex]
5. Round to the nearest cent:
- The total payment is already rounded to the nearest cent.
Thus, the interest accumulated over 90 days is [tex]$26.25, and the total payment required to pay off the promissory note is \( \$[/tex]726.25 \).
