Answer
$a.\quad 1500r^{3}+4500r^{2}+4500r+1500$
$b.\quad \$ 1,639.09$
Work Step by Step
a. $1500(1+r)(1+r)(1+r)$
...multiply the last pair of binomials, using FOIL.
$=1500(1+r)(1+r+r+r^{2})$
...gather like terms in the second parentheses.
$=1500(1+r)(r^{2}+2r+1)$
...multiply $1500(1+r)$
$=(1500+1500r)(r^{2}+2r+1)$
...distribute by making a table of products
$\left.\begin{array}{rlll}
& 1500 & +1500r & \\
\hline r^{2}| & 1500r^{2} & +1500r^{3} & \\
2r| & 3000r & +3000r^{2} & \\
1 |& 1500 & +1500r &
\end{array}\right.$
$=1500r^{2}+1500r^{3}+3000r+3000r^{2}+1500+1500r$
...gather like terms.
=$1500r^{3}+4500r^{2}+4500r+1500$
b. substitute: $r=0.03$
$1500(0.03)^{3}+4500(0.03)^{2}+4500(0.03)+1500$
$=1639.0905$
$=\$ 1,639.09$
