SOLUTION
Recall the simple interest formula
[tex]I=\frac{PRT}{100}[/tex]From the question
P=$8,865
R=?
The time is given as 75 days
Converting this to years gives
[tex]T=\frac{75}{365}[/tex]And the interest is
I=$82.60
Substitute these values into the interest formula
[tex]82.60=\frac{8865\times R\times\frac{75}{365}}{100}[/tex]Solve for R
[tex]\begin{gathered} 8260=8865\times R\times\frac{75}{365} \\ 8,260=R\frac{664875}{365} \\ 3014900=664875R \\ R=\frac{3014900}{664875} \\ R=4.53 \end{gathered}[/tex]Therefore the rate is 4.53%
