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Answer:
4%
Step-by-step explanation:
[tex]A = P(1+r/n)^{nt}[/tex]
A = final amount
P = initial amount
r = interest rate per time period
n = number of times compounded per time period
t = number of time period
A = 3932.82
r = what we want to find
n = 2
t = 6
[tex]A = P(1+r/n)^{nt}\\3932.82 = 3101(1+r/2)^{12}[/tex]
divide both sides by 3101 to isolate the exponent and its parts
[tex]3932.82/3101 = (1+r/2)^{12}[/tex]
put both sides to the power of (1/12) to help isolate the variable
[tex](3932.82/3101)^{1/12}= (1+r/2)[/tex]
subtract 1 from both sides to isolate the variable and its coefficient
[tex](3932.82/3101)^{1/12}-1= (r/2)[/tex]
multiply both sides by 2 to get r
[tex]((3932.82/3101)^{1/12}-1) * 2= r[/tex]
r ≈ 0.04 = 4%