Answer
See below:
Work Step by Step
(a).
Step 1: Rate is expressed as a decimal while calculating the interest. Thus, to convert the rate percent into a decimal, rate percent is divided by 100.
\[\begin{align}
& r=4.5percent \\
& =\frac{4.5}{100} \\
& =0.045
\end{align}\]
Step 2: The rate is divided by 12, because the amount is compounded monthly. So, n is taken as \[12\]. The amount can be computed by using the formula::
\[\begin{align}
& A=P{{\left( 1+\frac{r}{n} \right)}^{n\times t}} \\
& =\$4,500{{\left(1+\frac{0.045}{12}\right)}^{12\times3}}\\&=\$4,500\times{{\left(1.00375\right)}^{36}}\\&=\$5,149.116\end{align}\]
Step 3: Rounding off the amount to the nearest cent:
\[\$5,149.116=\$5,149.12\]
After rounding off the amount (A) to the nearest cent, the amount will become \[\$5,149.12\].
(b).
The interest can be computed by subtracting the original principal from the amount.
The amount of money calculated in the first part is\[\$5,149.12\].
Thus, to calculate the interest, following formula is used:
\[\begin{align}
& \text{Interest}=\text{Amount}-\text{Principal} \\
& =\$5,149.12-\$4,500\\&=\$649.12\end{align}\]
The interest calculated is \[\$649.12\].
