Answered

Liz Reynolds deposited [tex]\$2,000[/tex] into a savings account that pays [tex]8\%[/tex] compounded quarterly. Complete the table to compute the amount in the account after 1 year.

\begin{tabular}{|c|c|c|c|c|c|}
\hline
Original Principal & & & & & [tex]\$2,000.00[/tex] \\
\hline
Interest for First Quarter & [tex]\$2,000.00 \times 8\% \times \frac{1}{4}=[/tex] & [tex]\$40.00[/tex] & [tex]=[/tex] & [tex]+[/tex] & [tex]\$40.00[/tex] \\
\hline
Amount at End of First Quarter & [tex]\$2,000.00+\$40.00=[/tex] & & & & a. \\
\hline
Interest for Second Quarter & [tex]\$2,040.00 \times 8\% \times \frac{1}{4}=[/tex] & b. & [tex]=[/tex] & [tex]+[/tex] & c. \\
\hline
Amount at End of Second Quarter & & & & & d. \\
\hline
Interest for Third Quarter & & e. & [tex]=[/tex] & [tex]+[/tex] & f. \\
\hline
Amount at End of Third Quarter & & & & & g. \\
\hline
Interest for Fourth Quarter & & h. & [tex]=[/tex] & [tex]+[/tex] & i. \\
\hline
Amount at End of Fourth Quarter & & & & & j. \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's fill out the table step by step and calculate each value accordingly.

#### Table:
\begin{tabular}{|c|c|c|c|c|c|}
\hline Original Principal & & & & & [tex]$\$[/tex] 2,000.00[tex]$ \\ \hline Interest for First Quarter & $[/tex]\[tex]$ 2,000.00 \times 8 \% \times 1 / 4=$[/tex] & [tex]$\$[/tex] 40.00[tex]$ & $[/tex]=[tex]$ & + & $[/tex]\[tex]$ 40.00$[/tex] \\
\hline
Amount at End of First Quarter & [tex]$\$[/tex] 2,000.00 + \[tex]$ 40.00 =$[/tex] & [tex]$\$[/tex] 2,040.00[tex]$ & & & a. \\ \hline Interest for Second Quarter & $[/tex]\[tex]$ 2,040.00 \times 8 \% \times 1 / 4=$[/tex] & [tex]$\$[/tex] 40.80[tex]$ & $[/tex]=[tex]$ & + & b. \\ \hline \begin{tabular}{|l|} Amount at End of Second Quarter \\ \end{tabular} & $[/tex]\[tex]$ 2,040.00 + \$[/tex] 40.80 =[tex]$ & $[/tex]\[tex]$ 2,080.80 $[/tex] & & & c. \\
\hline
Interest for Third Quarter & [tex]$\$[/tex] 2,080.80 \times 8 \% \times 1 / 4=[tex]$ & $[/tex]\[tex]$ 41.62$[/tex] & [tex]$=$[/tex] & + & d. \\
\hline
Amount at End of Third Quarter & [tex]$\$[/tex] 2,080.80 + \[tex]$ 41.62 =$[/tex] & [tex]$\$[/tex] 2,122.42[tex]$ & & & e. \\ \hline Interest for Fourth Quarter & $[/tex]\[tex]$ 2,122.42 \times 8 \% \times 1 / 4=$[/tex] & [tex]$\$[/tex] 42.45[tex]$ & $[/tex]=[tex]$ & + & f. \\ \hline Amount at End of Fourth Quarter & $[/tex]\[tex]$ 2,122.42 + \$[/tex] 42.45 =[tex]$ & $[/tex]\[tex]$ 2,164.87$[/tex] & & & g. \\
\hline
\end{tabular}

#### Detailed Steps:

1. Original Principal: [tex]$\$[/tex] 2,000.00[tex]$ 2. Interest for First Quarter: \[ \$[/tex] 2,000.00 \times \frac{8\%}{4} = \[tex]$ 40.00 \] 3. Amount at End of First Quarter: \[ 2000.00 + 40.00 = \$[/tex] 2,040.00
\]
This value corresponds to [tex]$a.$[/tex]

4. Interest for Second Quarter:
[tex]\[ 2040.00 \times \frac{8\%}{4} = \$ 40.80 \][/tex]
This value corresponds to [tex]$b.$[/tex]

5. Amount at End of Second Quarter:
[tex]\[ 2040.00 + 40.80 = \$ 2,080.80 \][/tex]
This value corresponds to [tex]$c.$[/tex]

6. Interest for Third Quarter:
[tex]\[ 2080.80 \times \frac{8\%}{4} = \$ 41.62 \][/tex]
This value corresponds to [tex]$d.$[/tex]

7. Amount at End of Third Quarter:
[tex]\[ 2080.80 + 41.62 = \$ 2,122.42 \][/tex]
This value corresponds to [tex]$e.$[/tex]

8. Interest for Fourth Quarter:
[tex]\[ 2122.42 \times \frac{8\%}{4} = \$ 42.45 \][/tex]
This value corresponds to [tex]$f.$[/tex]

9. Amount at End of Fourth Quarter:
[tex]\[ 2122.42 + 42.45 = \$ 2,164.87 \][/tex]
This value corresponds to [tex]$g.$[/tex]

The filled-out table should look like this:

\begin{tabular}{|c|c|c|c|c|c|}
\hline Original Principal & & & & & [tex]$\$[/tex] 2,000.00[tex]$ \\ \hline Interest for First Quarter & $[/tex]\[tex]$ 2,000.00 \times 8 \% \times 1 / 4=$[/tex] & [tex]$\$[/tex] 40.00[tex]$ & $[/tex]=[tex]$ & + & $[/tex]\[tex]$ 40.00$[/tex] \\
\hline
Amount at End of First Quarter & [tex]$\$[/tex] 2,000.00 + \[tex]$ 40.00 =$[/tex] & [tex]$\$[/tex] 2,040.00[tex]$ & & & $[/tex]\ 2,040.00[tex]$ \\ \hline Interest for Second Quarter & $[/tex]\[tex]$ 2,040.00 \times 8 \% \times 1 / 4=$[/tex] & [tex]$\$[/tex] 40.80[tex]$ & $[/tex]=[tex]$ & + & \$[/tex] 40.80 \\
\hline
\begin{tabular}{|l|}
Amount at End of Second Quarter \\
\end{tabular} & [tex]$\$[/tex] 2,040.00 + \[tex]$ 40.80 =$[/tex] & [tex]$\$[/tex] 2,080.80 [tex]$ & & & \$[/tex] 2,080.80 \\
\hline
Interest for Third Quarter & [tex]$\$[/tex] 2,080.80 \times 8 \% \times 1 / 4=[tex]$ & $[/tex]\[tex]$ 41.62$[/tex] & [tex]$=$[/tex] & + & \[tex]$ 41.62 \\ \hline Amount at End of Third Quarter & $[/tex]\[tex]$ 2,080.80 + \$[/tex] 41.62 =[tex]$ & $[/tex]\[tex]$ 2,122.42$[/tex] & & & \[tex]$ 2,122.42 \\ \hline Interest for Fourth Quarter & $[/tex]\[tex]$ 2,122.42 \times 8 \% \times 1 / 4=$[/tex] & [tex]$\$[/tex] 42.45[tex]$ & $[/tex]=[tex]$ & + & \$[/tex] 42.45 \\
\hline
Amount at End of Fourth Quarter & [tex]$\$[/tex] 2,122.42 + \[tex]$ 42.45 =$[/tex] & [tex]$\$[/tex] 2,164.87[tex]$ & & & \$[/tex] 2,164.87 \\
\hline
\end{tabular}

This table provides a detailed breakdown of each interest calculation and the resulting amounts at the end of each quarter.