Answer
C. $7.52
Explanation
To solve this, we are going to use the compounded interest formula:
@@MATH_TOKEN_0@@
where
@@MATH_TOKEN_1@@ is the final amount after @@MATH_TOKEN_2@@ years
@@MATH_TOKEN_3@@ is the initial investment
@@MATH_TOKEN_4@@ is the interest rate in decimal form
@@MATH_TOKEN_5@@ is the number of times the interest is compounded per year
@@MATH_TOKEN_6@@ is the time in years
We know that the initial investment is $2000 and the time is 2 years, so \(P=2000\) and \(t=2\). Now, for the the first account \(n=2\) and \(r=\frac{4.6}{100} =0.046\); for the second account \(n=4\) and \(r=\frac{4.4}{100} =0.044\). Let's calculate \(A\) for both accounts:
For the first account
\(A=2000(1+\frac{0.046}{2} )^{(2)(2)}\)
\(A=2000(1+\frac{0.046}{2} )^{4}\)
\(A=2190.45\)
For the second account
\(A=2000(1+\frac{0.044}{4} )^{(4)(2)}\)
\(A=2000(1+\frac{0.044}{4} )^{8}\)
\(A=2182.93\)
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.
