Answer :
This is compound interest problem. The compound interest formula is:
[tex]F=P(1+r)^t[/tex]Where
F is the future amount [we want this, after 9 years]
P is the initial amount [$400, in our case]
r is the rate of interest per period [8% per year. Since per quarter compounding, we want interest rate per quarter, so, 8%/4 = 2%. In decimal, 2/100 = 0.02]
t is the time period [number of compoundings in 9 year would be 9*4 = 36]
We now know the given information, we simply substitute it into the formula and solve for F. Shown below:
[tex]\begin{gathered} F=P(1+r)^t \\ F=400(1+0.02)^{36} \\ F=400(1.02)^{36} \\ F=815.95 \end{gathered}[/tex]The account will be worth $815.95 after 9 years!