Answer
C. $7.52
Explanation
To solve this, we are going to use the compounded interest formula:
[tex]A=P(1+ \frac{r}{n} )^{nt}[/tex]
where
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the time in years
We know that the initial investment is $2000 and the time is 2 years, so [tex]P=2000[/tex] and [tex]t=2[/tex]. Now, for the the first account [tex]n=2[/tex] and [tex]r=\frac{4.6}{100} =0.046[/tex]; for the second account [tex]n=4[/tex] and [tex]r=\frac{4.4}{100} =0.044[/tex]. Let's calculate [tex]A[/tex] for both accounts:
For the first account
[tex]A=2000(1+\frac{0.046}{2} )^{(2)(2)}[/tex]
[tex]A=2000(1+\frac{0.046}{2} )^{4}[/tex]
[tex]A=2190.45[/tex]
For the second account
[tex]A=2000(1+\frac{0.044}{4} )^{(4)(2)}[/tex]
[tex]A=2000(1+\frac{0.044}{4} )^{8}[/tex]
[tex]A=2182.93[/tex]
Now we just need to subtract the total amount of the second account from the total amount of the first account:
$2190.45 - $2182.93 = $7.52
The account of 4.6 compounded semiannually earn $7.52 more than the account of 4.4% compounded quarterly.
