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At the age of 28, you decide to invest in a 20-Year Endowment insurance policy. The face value for the policy that you are interested in is [tex]$\$[/tex] 91,500[tex]$. Using the provided table, determine the annual premium for a 28-year-old healthy female seeking a 20-Year Endowment. Round your answer to the nearest cent where necessary.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline \multirow{3}{*}{ Age } & \multicolumn{6}{|c|}{ Permanent Insurance } \\
\cline { 2 - 7 } & \multicolumn{2}{|c|}{\begin{tabular}{c}
Whole Life \\
20-Payment \\
Life
\end{tabular}} & \multicolumn{2}{c|}{\begin{tabular}{c}
20-Year \\
Endowment
\end{tabular}} \\
\cline { 2 - 7 } & Male & Female & Male & Female & Male & Female \\
\hline 25 & $[/tex]\[tex]$ 16.38$[/tex] & [tex]$\$[/tex] 14.38[tex]$ & $[/tex]\[tex]$ 28.40$[/tex] & [tex]$\$[/tex] 25.04[tex]$ & $[/tex]\[tex]$ 37.02$[/tex] & [tex]$\$[/tex] 34.87[tex]$ \\
\hline 26 & $[/tex]\[tex]$ 16.91$[/tex] & [tex]$\$[/tex] 14.77[tex]$ & $[/tex]\[tex]$ 29.11$[/tex] & [tex]$\$[/tex] 25.96[tex]$ & $[/tex]\[tex]$ 37.67$[/tex] & [tex]$\$[/tex] 35.30[tex]$ \\
\hline 27 & $[/tex]\[tex]$ 17.27$[/tex] & [tex]$\$[/tex] 15.23[tex]$ & $[/tex]\[tex]$ 29.97$[/tex] & [tex]$\$[/tex] 26.83[tex]$ & $[/tex]\[tex]$ 38.23$[/tex] & [tex]$\$[/tex] 35.96[tex]$ \\
\hline 28 & $[/tex]\[tex]$ 17.76$[/tex] & [tex]$\$[/tex] 15.66[tex]$ & $[/tex]\[tex]$ 30.68$[/tex] & [tex]$\$[/tex] 27.54[tex]$ & $[/tex]\[tex]$ 38.96$[/tex] & [tex]$\$[/tex] 36.44[tex]$ \\
\hline
\end{tabular}

a. $[/tex]\[tex]$ 3,334.26$[/tex]

b. [tex]$\$[/tex] 3,290.34[tex]$

c. $[/tex]\[tex]$ 3,229.95$[/tex]

d. [tex]$\$[/tex] 3,190.61$

Please select the best answer from the choices provided:
A
B
C
D


Sagot :

To determine the annual premium for a 28-year-old healthy female seeking a 20-Year Endowment insurance policy with a face value of \[tex]$91,500, we proceed as follows: 1. Identify the premium rate from the table: - For a 28-year-old healthy female, the premium rate for a 20-Year Endowment policy is \$[/tex]36.44 per \[tex]$1000 of face value. 2. Calculate the premium rate as a fraction of the face value: - The premium rate is \$[/tex]36.44 per \[tex]$1000, which translates to 0.03644 (as a decimal). 3. Calculate the annual premium using the given face value: - The face value of the policy is \$[/tex]91,500.
- To find the annual premium, multiply the face value by the premium rate per unit:
[tex]\[ \text{Annual Premium} = 91,500 \times 0.03644 \][/tex]

4. Perform the multiplication:
- Multiplying 91,500 by 0.03644:
[tex]\[ 91,500 \times 0.03644 = 3,334.26 \][/tex]

5. Round the result to the nearest cent if necessary:
- The result is already in cent form: \[tex]$3,334.26. 6. Compare the calculated annual premium to the given options: - a. \$[/tex]3,334.26
- b. \[tex]$3,290.34 - c. \$[/tex]3,229.95
- d. \[tex]$3,190.61 The calculated annual premium (\$[/tex]3,334.26) exactly matches option a.

Therefore, the best answer is option a: [tex]$\$[/tex]3,334.26$.
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