Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Ask your questions and receive precise answers from experienced professionals across different disciplines. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
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}
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
