The formula we need here is [tex]A(t)=P(1+ \frac{r}{n}) ^{nt} [/tex], where A(t) is the amount at the end of it all, P is the initial investment, n is the number of times the money is compounded (I'll explain in a sec), and t is the time we invest our money in years. Going back to n, if the money is invested for 1 year, n = 1 because it is compounded once; if the money is invested for 6 months, n = 2 (twice a year the money is compounded), if n = 4, the money is compounded quarterly; if n = 52, the money is compounded weekly. See? For us, the equation is filled in with these values: P = 9250, r = 7% or .07, t = 5, n = 52. [tex]A(t)=9250(1+ \frac{.07}{52})^{(52)(5) [/tex] which simplifies a bit to [tex]A(t)=9250(1+.0013461538)^{260}[/tex]. Doing the adding inside the parenthesis we have [tex]A(t)=9250(1.0013461538)^{260}[/tex]. Raise the parenthesis value to the exponent of 260 to get A(t)=9250(1.418733571) . Now we can find the amount we will have after 5 years of "growing" $9,250 that's compounded weekly at a rate of 7%. A(t) = $13,123.2, last choice above.
