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Tim Tradesman pays \[tex]$2,000 annually for \$[/tex]150,000 worth of life insurance. Answer the following questions.

Cash Value of the Insurance Policy

\begin{tabular}{|c|c|}
\hline Policy Anniversary & Cash Value Per Unit \\
\hline 5th year & \[tex]$30.00 \\
\hline 10th year & \$[/tex]89.00 \\
\hline 15th year & \[tex]$160.00 \\
\hline 20th year & \$[/tex]232.00 \\
\hline 25th year & \[tex]$340.00 \\
\hline
\end{tabular}

a. At the end of 10 years, how much will Tim have paid in premiums? $[/tex]\square[tex]$

b. At the end of 10 years, what will the cash value of his policy be? $[/tex]\square[tex]$

c. What will the ratio of cash value to premiums paid be (as a percent)? $[/tex]\square$



Answer :

GinnyAnswer
Sure, let’s go through each part of the question step by step.

Part (a): At the end of 10 years, how much will Tim have paid in premiums?

1. Tim pays an annual premium of [tex]$2000. 2. The policy duration given is 10 years. 3. To find the total premiums paid over 10 years, we multiply the annual premium by the number of years. So, the total premiums paid = \$[/tex]2000 [tex]\(\times\)[/tex] 10 years = \[tex]$20000 Answer for Part (a): \$[/tex]20000

Part (b): At the end of 10 years, what will the cash value of his policy be?

1. From the given table, the cash value per unit after 10 years is \[tex]$89. 2. Since the question pertains specifically to the cash value after 10 years, we use this directly. Answer for Part (b): \$[/tex]89

Part (c): What will the ratio of cash value to premiums paid be (as a percent)?

1. To find the ratio of the cash value to premiums paid, we divide the cash value after 10 years by the total premiums paid and then convert it to a percentage.
2. Cash value after 10 years is \[tex]$89. 3. Total premiums paid over 10 years is \$[/tex]20000.
4. The ratio is given by:
[tex]\[ \text{Ratio} = \left(\frac{\$89}{\$20000}\right) \times 100 \][/tex]

[tex]\[ \text{Ratio} = 0.445\% \][/tex]

Answer for Part (c): 0.445%

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