We have to calculate the outstanding principal of the loan.
The interest for the period is $223.75, where the period goes from September 28 to December 14.
The rate of interest is 5%, so r = 0.05.
The period includes 3 days of September, 31 days of October, 30 days of November and 14 days of December.
This is a total of 78 days.
We can now relate all the concepts as:
[tex]I=C\cdot r\cdot t[/tex]Where I = 223.75, r = 0.05 and t = 78/365.
We then can calculate C as:
[tex]\begin{gathered} C=\frac{I}{r\cdot t} \\ C=\frac{223.75}{0.05\cdot\frac{78}{360}} \\ C\approx\frac{223.75}{0.05\cdot0.214} \\ C\approx\frac{223.75}{0.0107} \\ C\approx20911.21 \end{gathered}[/tex]Answer: the principal is approximately $20,911.21.
