To determine the total payment required to pay off a promissory note issued for \$500.00 at a 10% ordinary interest rate for a term of 180 days, we follow these steps:
1. Understand the Simple Interest Formula:
The simple interest formula is given by:
[tex]\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\][/tex]
2. Convert the Interest Rate to a Decimal:
The annual interest rate is 10%. To use this in our calculations, we need to express it as a decimal:
[tex]\[
\text{Rate} = \frac{10}{100} = 0.10
\][/tex]
3. Convert the Time Period to a Fraction of a Year:
Since the term is given in days and ordinary interest assumes a 360-day year, we convert the term to a fraction of a year as follows:
[tex]\[
\text{Time} = \frac{\text{Term in Days}}{\text{Days in a Year}} = \frac{180}{360} = 0.5
\][/tex]
4. Calculate the Interest:
Substitute the known values into the simple interest formula:
[tex]\[
\text{Interest} = 500.00 \times 0.10 \times 0.5
\][/tex]
Perform the multiplication:
[tex]\[
\text{Interest} = 500.00 \times 0.05 = 25.00
\][/tex]
5. Calculate the Total Payment:
The total payment includes both the principal amount and the interest:
[tex]\[
\text{Total Payment} = \text{Principal} + \text{Interest} = 500.00 + 25.00 = 525.00
\][/tex]
6. Round to the Nearest Cent (if necessary):
In this case, the values already reflect amounts rounded to the nearest cent.
Therefore, the total payment required to pay off the promissory note is:
[tex]\[
\boxed{525.00}
\][/tex]
