#### Answer

Ted would have $\$8,699.69$ at the end of five years.

#### Work Step by Step

Find the total value (A) using the formula $A=P\left(1+\dfrac{r}{n}\right)^{nt}$ where $P$=principal amount, $r=$annual interest rate, $t$=time in years, and $n$=number of compounding periods in a year
The given problem has:
$P=\$6,000$
$t=5$
$r=7.5\%$
$n=4$ (since compounded quarterly)
Use the formula above to obtain:
$A=\$6,000\left(1+\dfrac{7.5\%}{4}\right)^{4(5)}
\\A=\$6,000\left(1+\dfrac{0.075}{4}\right)^{20}
\\A=\$8,699.688154
\\A\approx \$8,699.69$