Answer
(a) The student must pay interest of $\$247.50$
(b) The future value of the loan is $\$4247.50$
Work Step by Step
(a) With simple interest, this is the formula we use to calculate the amount of interest, $I$.
$I = P~r~t$
$P$ is the present value
$r$ is the interest rate
$t$ is the number of years
We can calculate the interest.
$I = P~r~t$
$I = (\$4000)(0.0825)(0.75)$
$I = \$247.50$
The student must pay interest of $\$247.50$
(b) The future value of the loan is the present value plus the interest.
$A = P + I$
$A = \$4000 + \$247.50$
$A = \$4247.50$
The future value of the loan is $\$4247.50$
