Answer :
The simple interest formula allows us to calculate the interest earned or paid on a loan. According to this formula, the amount of interest is given by I = C · i · t, where C is the principal, i is the annual interest rate in decimal form, and t is the period of time expressed in years.
[tex]I=C\cdot t\cdot i[/tex]Where:
• I = interest
,• C= initial capital
,• t = time in years
,• i =annual interest
From the problem we have
[tex]\begin{gathered} C=5000 \\ i=0.15 \\ I=5000\cdot(0.15)\cdot t \\ I=750\cdot t \end{gathered}[/tex]The loans for Keen and Kyle differ in time so we will calculate the interest of both loans
[tex]\begin{gathered} I=750\cdot(3.5) \\ I=2625\to Keen \end{gathered}[/tex][tex]\begin{gathered} I=750\cdot(5) \\ I=3750\to Kyle \end{gathered}[/tex]To find the difference, we subtract the interest values that Keen and Kyle paid to Mrs. Cruz.
[tex]3750-2625=1125[/tex]