For the interest calculation we shall apply the simple interest formula which is;
[tex]\begin{gathered} I=P\times R\times T \\ \text{Where;} \\ P=\text{Initial amount borrowed} \\ R=\text{rate of interest (expressed as decimal)} \\ T=\text{Time in years} \end{gathered}[/tex]The initial amount is $21890, the rate is 14% (that is 0.14) and the time is 164/365 of a year.
Therefore, the interest calculated would be;
[tex]\begin{gathered} I=P\times R\times T \\ I=21890\times0.14\times\frac{164}{365} \\ I=3064.6\times\frac{164}{365} \\ I=1376.9709589 \\ I\approx1376.9\text{ (rounded to the nearest cent)} \end{gathered}[/tex]The interest payable at the end of 164 days is $1,376.90 (rounded to the nearest cent).
Therefore, the amount Juan would pay back is;
