Answer
See below
Work Step by Step
(a)
Calculation of the simple interest can be done by multiplying the principal amount with the rate of interest and respective duration of time.
Compute the simple interest as mentioned below:
\[\begin{align}
& \text{Simple interest}=P\times r\times t \\
& =\$3500\times0.105\times0.3333\\&\approx\$122.50\end{align}\]
Hence, the simple interest that is paid by the student is \[\$122.50\].
(b)
Calculation of future value of loan can be done with the mentioned formula:
\[A=P\times \left( 1+rt \right)\]
where A denotes the future value of the amount, P denotes the principal amount, r denotes the rate of interest, and t denotes the number of years.
Compute the future value by substituting the values in the formula as mentioned below:
\[\begin{align}
& A=P\times \left( 1+rt \right) \\
& =\$3500\times\left(1+\left(0.105\times\frac{1}{3}\right)\right)\\&=\$3500\times\left(1+0.035\right)\\&=\$3622.50\end{align}\]
Hence, the future value of the loan is \[\$3622.50\].
