First part:
P = $5100
r = 8.2% = 8.2/100 = 0.082
t = 3 years
The rule of the simple interest is
[tex]I=\text{prt}[/tex]Substitute the given value in the rule
[tex]\begin{gathered} I=5100(0.082)(3) \\ I=\text{ \$1254.6} \end{gathered}[/tex]The interest at the end of 3 years for a simple interest loan is $1254.60
Second part:
P = $3500
r = 6.7% = 6.7/100 = 0.067
t = 9 years
The rule of the end amount is
[tex]A=P(1+rt)[/tex]Substitute the given values in the rule
[tex]\begin{gathered} A=3500(1+0.067\times9) \\ A=\text{ \$5610.50} \end{gathered}[/tex]The total at the end of 9 years for a simple interest loan is $5610.50