First, divide the annual interest rate by 2 to find the semiannual interest rate:
[tex]\frac{5.5}{2}=2.75[/tex]
Next, identify the number of periods when the 2.75% increase will be appliad. In a period of 10 years, there are 20 semiannual periods.
Each period, the initial investment gets multiplied by a factor of:
[tex]1+\frac{2.75}{100}=1+0.0275=1.0275[/tex]
Over 20 semiannual periods, the initial investment will get multiplied by a factor of:
[tex]1.0275^{20}[/tex]
Therefore, after 10 years, the amount of money in the account is:
[tex]\begin{gathered} 4000\times(1.0275)^{20}=4000\times1.7204\ldots \\ =6881.7137\ldots \end{gathered}[/tex]
To the nearest cent, the amount of money in the account will be:
[tex]6881.71[/tex]
