Sofia's account balance in 7 years will be $11,726.12
From the question, we are to determine Sofia's account balance in 7 years
Using the compound interest formula,
[tex]A = P(1+ \frac{r}{n} )^{nt}[/tex]
Where A is the amount
P is the principal
r is the rate
n is the number of times compounded
and t is the time in years
From the given information,
P = $8,000
r = 5.5% = 0.055
n = 4
t = 7
Putting the parameters into the equation, we get
[tex]A = 8000(1+ \frac{0.055}{4} )^{4\times 7}[/tex]
[tex]A = 8000 ( 1+ 0.01375)^{28}[/tex]
[tex]A = 8000 ( 1.01375)^{28}[/tex]
A = $11,726.12
Hence, Sofia's account balance in 7 years will be $11,726.12
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