To find the total payment required to pay off a promissory note, we first need to calculate the interest incurred over the 180-day term and then add it to the principal amount. Here's how to do it:
1. Calculate the Interest:
Given that the principal amount (P) of the promissory note is [tex]$600, the annual interest rate (r) is 8%, and the term of the note (T) is 180 days, we use the formula for ordinary interest (I) as follows:
\[
I = P \times r \times \frac{T}{D}
\]
Here,
\( P = $[/tex]600 \) (principal),
[tex]\( r = 8\% = 0.08 \)[/tex] (interest rate as a decimal),
[tex]\( T = 180 \)[/tex] days (term of the note), and
[tex]\( D = 360 \)[/tex] days (ordinary interest is typically based on a 360-day year).
Let's use these values:
[tex]\[
I = $600 \times 0.08 \times \frac{180}{360}
\][/tex]
[tex]\[
I = $600 \times 0.08 \times 0.5
\][/tex]
[tex]\[
I = $600 \times 0.04
\][/tex]
[tex]\[
I = $24
\][/tex]
So, the interest is [tex]$24.
2. Calculate the Total Payment:
To find the total payment required to pay off the note, add the principal amount to the interest:
\[
\text{Total Payment} = P + I
\]
\[
\text{Total Payment} = $[/tex]600 + [tex]$24
\]
\[
\text{Total Payment} = $[/tex]624
\]
3. Rounding:
Since the total payment resulting from the calculation is already to the nearest cent, no additional rounding is necessary.
Therefore, the total payment required to pay off the promissory note is $624.
