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Sagot :
To complete the table using the provided numerical results, let us break down each entry step-by-step:
1. [tex]$\$[/tex] 5,000[tex]$ deposit at $[/tex]6.00\%[tex]$, compounded quarterly, for $[/tex]2[tex]$ years: - Number of Periods: \( 4 \times 2 = 8 \) - Rate per Period: \( 0.06 / 4 = 0.015 \) - Table Value: \( 8.432839106353745 \) - FV of Ordinary Annuity: \( 5000 \times 8.432839106353745 = 42164.195531768724 \) - Interest Earned: \( 42164.195531768724 - (5000 \times 8) = 2164.1955317687243 \) - FV of Annuity Due: \( 42164.195531768724 \times (1 + 0.015) = 42796.658464745255 \) 2. $[/tex]\[tex]$ 800$[/tex] deposit at [tex]$4.00\%$[/tex], compounded semiannually, for [tex]$6$[/tex] years:
- Number of Periods: [tex]\( 2 \times 6 = 12 \)[/tex]
- Rate per Period: [tex]\( 0.04 / 2 = 0.02 \)[/tex]
- Table Value: [tex]\( 13.412089728127274 \)[/tex]
- FV of Ordinary Annuity: [tex]\( 800 \times 13.412089728127274 = 10729.671782501819 \)[/tex]
- Interest Earned: [tex]\( 10729.671782501819 - (800 \times 12) = 1129.6717825018186 \)[/tex]
- FV of Annuity Due: [tex]\( 10729.671782501819 \times (1 + 0.02) = 10944.265218151855 \)[/tex]
3. [tex]$\$[/tex] 2,000[tex]$ deposit at $[/tex]4.00\%[tex]$, compounded annually, for $[/tex]10[tex]$ years: - Number of Periods: \( 1 \times 10 = 10 \) - Rate per Period: \( 0.04 / 1 = 0.04 \) - Table Value: \( 12.006107122958609 \) - FV of Ordinary Annuity: \( 2000 \times 12.006107122958609 = 24012.214245917217 \) - Interest Earned: \( 24012.214245917217 - (2000 \times 10) = 4012.2142459172173 \) - FV of Annuity Due: \( 24012.214245917217 \times (1 + 0.04) = 24972.702815753906 \) 4. $[/tex]\[tex]$ 1,000$[/tex] deposit at [tex]$6.00\%$[/tex], compounded monthly, for [tex]$3$[/tex] years:
- Number of Periods: [tex]\( 12 \times 3 = 36 \)[/tex]
- Rate per Period: [tex]\( 0.06 / 12 = 0.005 \)[/tex]
- Table Value: [tex]\( 39.33610496468294 \)[/tex]
- FV of Ordinary Annuity: [tex]\( 1000 \times 39.33610496468294 = 39336.10496468294 \)[/tex]
- Interest Earned: [tex]\( 39336.10496468294 - (1000 \times 36) = 3336.1049646829415 \)[/tex]
- FV of Annuity Due: [tex]\( 39336.10496468294 \times (1 + 0.005) = 39532.78548950635 \)[/tex]
Here is the completed table:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline Deposit & Rate & Compounded & Years & \begin{tabular}{l}
Number \\
of \\
Periods
\end{tabular} & \begin{tabular}{l}
Rate \\
per \\
Period
\end{tabular} & \begin{tabular}{l}
Table \\
Value
\end{tabular} & \begin{tabular}{l}
FV of \\
Ordinary \\
Annuity
\end{tabular} & \begin{tabular}{l}
Interest \\
Earned
\end{tabular} & \begin{tabular}{l}
FV of \\
Annuity Due
\end{tabular} \\
\hline[tex]$\$[/tex] 5,000[tex]$ & $[/tex]6.00 \%[tex]$ & Quarterly & 2 & 8 & 0.015 & 8.432839106353745 & 42164.195531768724 & 2164.1955317687243 & 42796.658464745255 \\ \hline$[/tex]\[tex]$ 800$[/tex] & [tex]$4.00 \%$[/tex] & Semiannually & 6 & 12 & 0.02 & 13.412089728127274 & 10729.671782501819 & 1129.6717825018186 & 10944.265218151855 \\
\hline[tex]$\$[/tex] 2,000[tex]$ & $[/tex]4.00 \%[tex]$ & Annually & 10 & 10 & 0.04 & 12.006107122958609 & 24012.214245917217 & 4012.2142459172173 & 24972.702815753906 \\ \hline$[/tex]\[tex]$ 1,000$[/tex] & [tex]$6.00 \%$[/tex] & Monthly & 3 & 36 & 0.005 & 39.33610496468294 & 39336.10496468294 & 3336.1049646829415 & 39532.78548950635 \\
\hline
\end{tabular}
1. [tex]$\$[/tex] 5,000[tex]$ deposit at $[/tex]6.00\%[tex]$, compounded quarterly, for $[/tex]2[tex]$ years: - Number of Periods: \( 4 \times 2 = 8 \) - Rate per Period: \( 0.06 / 4 = 0.015 \) - Table Value: \( 8.432839106353745 \) - FV of Ordinary Annuity: \( 5000 \times 8.432839106353745 = 42164.195531768724 \) - Interest Earned: \( 42164.195531768724 - (5000 \times 8) = 2164.1955317687243 \) - FV of Annuity Due: \( 42164.195531768724 \times (1 + 0.015) = 42796.658464745255 \) 2. $[/tex]\[tex]$ 800$[/tex] deposit at [tex]$4.00\%$[/tex], compounded semiannually, for [tex]$6$[/tex] years:
- Number of Periods: [tex]\( 2 \times 6 = 12 \)[/tex]
- Rate per Period: [tex]\( 0.04 / 2 = 0.02 \)[/tex]
- Table Value: [tex]\( 13.412089728127274 \)[/tex]
- FV of Ordinary Annuity: [tex]\( 800 \times 13.412089728127274 = 10729.671782501819 \)[/tex]
- Interest Earned: [tex]\( 10729.671782501819 - (800 \times 12) = 1129.6717825018186 \)[/tex]
- FV of Annuity Due: [tex]\( 10729.671782501819 \times (1 + 0.02) = 10944.265218151855 \)[/tex]
3. [tex]$\$[/tex] 2,000[tex]$ deposit at $[/tex]4.00\%[tex]$, compounded annually, for $[/tex]10[tex]$ years: - Number of Periods: \( 1 \times 10 = 10 \) - Rate per Period: \( 0.04 / 1 = 0.04 \) - Table Value: \( 12.006107122958609 \) - FV of Ordinary Annuity: \( 2000 \times 12.006107122958609 = 24012.214245917217 \) - Interest Earned: \( 24012.214245917217 - (2000 \times 10) = 4012.2142459172173 \) - FV of Annuity Due: \( 24012.214245917217 \times (1 + 0.04) = 24972.702815753906 \) 4. $[/tex]\[tex]$ 1,000$[/tex] deposit at [tex]$6.00\%$[/tex], compounded monthly, for [tex]$3$[/tex] years:
- Number of Periods: [tex]\( 12 \times 3 = 36 \)[/tex]
- Rate per Period: [tex]\( 0.06 / 12 = 0.005 \)[/tex]
- Table Value: [tex]\( 39.33610496468294 \)[/tex]
- FV of Ordinary Annuity: [tex]\( 1000 \times 39.33610496468294 = 39336.10496468294 \)[/tex]
- Interest Earned: [tex]\( 39336.10496468294 - (1000 \times 36) = 3336.1049646829415 \)[/tex]
- FV of Annuity Due: [tex]\( 39336.10496468294 \times (1 + 0.005) = 39532.78548950635 \)[/tex]
Here is the completed table:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline Deposit & Rate & Compounded & Years & \begin{tabular}{l}
Number \\
of \\
Periods
\end{tabular} & \begin{tabular}{l}
Rate \\
per \\
Period
\end{tabular} & \begin{tabular}{l}
Table \\
Value
\end{tabular} & \begin{tabular}{l}
FV of \\
Ordinary \\
Annuity
\end{tabular} & \begin{tabular}{l}
Interest \\
Earned
\end{tabular} & \begin{tabular}{l}
FV of \\
Annuity Due
\end{tabular} \\
\hline[tex]$\$[/tex] 5,000[tex]$ & $[/tex]6.00 \%[tex]$ & Quarterly & 2 & 8 & 0.015 & 8.432839106353745 & 42164.195531768724 & 2164.1955317687243 & 42796.658464745255 \\ \hline$[/tex]\[tex]$ 800$[/tex] & [tex]$4.00 \%$[/tex] & Semiannually & 6 & 12 & 0.02 & 13.412089728127274 & 10729.671782501819 & 1129.6717825018186 & 10944.265218151855 \\
\hline[tex]$\$[/tex] 2,000[tex]$ & $[/tex]4.00 \%[tex]$ & Annually & 10 & 10 & 0.04 & 12.006107122958609 & 24012.214245917217 & 4012.2142459172173 & 24972.702815753906 \\ \hline$[/tex]\[tex]$ 1,000$[/tex] & [tex]$6.00 \%$[/tex] & Monthly & 3 & 36 & 0.005 & 39.33610496468294 & 39336.10496468294 & 3336.1049646829415 & 39532.78548950635 \\
\hline
\end{tabular}
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