Answer :
To complete the table for the given problem, we will determine the final value of the investment over three years, compounding annually at a rate of 9%.
### First Year
- Initial Principal: \[tex]$3300 - Interest Earned: \[ 3300 \times 0.09 = \$[/tex]297
\]
- Total Balance:
[tex]\[ 3300 + 297 = \$3597 \][/tex]
Thus, the table for the first year:
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \end{array} \][/tex]
### Second Year
- Principal at the start of the year: \[tex]$3597 - Interest Earned: \[ 3597 \times 0.09 = \$[/tex]323.73
\]
- Total Balance:
[tex]\[ 3597 + 323.73 = \$3920.73 \][/tex]
Thus, the table for the second year:
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \text{Second year} & \$3300 + \$297 & \$3597 & \$323.73 \\ \end{array} \][/tex]
### Third Year
- Principal at the start of the year: \[tex]$3920.73 - Interest Earned: \[ 3920.73 \times 0.09 = \$[/tex]352.87
\]
- Total Balance:
[tex]\[ 3920.73 + 352.87 = \$4273.60 \][/tex]
Thus, the table for the third year:
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \text{Second year} & \$3300 + \$297 & \$3597 & \$323.73 \\ \text{Third year} & \$3597 + \$323.73 & \$3920.73 & \$352.87 \\ \end{array} \][/tex]
### Summary Table
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \text{Second year} & \$3300 + \$297 & \$3597 & \$323.73 \\ \text{Third year} & \$3597 + \$323.73 & \$3920.73 & \$352.87 \\ \end{array} \][/tex]
By the end of the third year, the final value of the investment is \$4273.60.
### First Year
- Initial Principal: \[tex]$3300 - Interest Earned: \[ 3300 \times 0.09 = \$[/tex]297
\]
- Total Balance:
[tex]\[ 3300 + 297 = \$3597 \][/tex]
Thus, the table for the first year:
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \end{array} \][/tex]
### Second Year
- Principal at the start of the year: \[tex]$3597 - Interest Earned: \[ 3597 \times 0.09 = \$[/tex]323.73
\]
- Total Balance:
[tex]\[ 3597 + 323.73 = \$3920.73 \][/tex]
Thus, the table for the second year:
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \text{Second year} & \$3300 + \$297 & \$3597 & \$323.73 \\ \end{array} \][/tex]
### Third Year
- Principal at the start of the year: \[tex]$3920.73 - Interest Earned: \[ 3920.73 \times 0.09 = \$[/tex]352.87
\]
- Total Balance:
[tex]\[ 3920.73 + 352.87 = \$4273.60 \][/tex]
Thus, the table for the third year:
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \text{Second year} & \$3300 + \$297 & \$3597 & \$323.73 \\ \text{Third year} & \$3597 + \$323.73 & \$3920.73 & \$352.87 \\ \end{array} \][/tex]
### Summary Table
[tex]\[ \begin{array}{lccc} & \text{Balance + interest} & \text{Total balance} & \text{Interest earned} \\ \text{First year} & - & \$3300 & \$297 \\ \text{Second year} & \$3300 + \$297 & \$3597 & \$323.73 \\ \text{Third year} & \$3597 + \$323.73 & \$3920.73 & \$352.87 \\ \end{array} \][/tex]
By the end of the third year, the final value of the investment is \$4273.60.
