Let's go through each of the questions step by step:
a. At the end of 10 years, how much will Tim have paid in premiums?
Tim pays an annual premium of \[tex]$2,000 for his life insurance policy. To calculate the total amount paid in premiums over 10 years, we need to multiply the annual premium by the number of years:
\[
\text{Total premiums paid} = \text{Annual premium} \times \text{Number of years} = 2000 \, \text{USD/year} \times 10 \, \text{years} = 20,000 \, \text{USD}
\]
So, Tim will have paid \$[/tex]20,000 in premiums over 10 years.
b. At the end of 10 years, what will the cash value of his policy be?
According to the table, the cash value per unit at the end of 10 years is \[tex]$89. Assuming that this value is indicative of the entire policy, the cash value of his policy at the end of 10 years is therefore:
\[
\text{Cash value} = 89 \, \text{USD}
\]
So, the cash value of his policy at the end of 10 years will be \$[/tex]89.
c. What will the ratio of cash value to premiums paid be (as a percent)?
To find the ratio of the cash value to the premiums paid, we divide the cash value by the total premiums paid and then convert this ratio to a percentage:
[tex]\[
\text{Ratio (as a percent)} = \left( \frac{\text{Cash value}}{\text{Total premiums paid}} \right) \times 100 = \left( \frac{89 \, \text{USD}}{20,000 \, \text{USD}} \right) \times 100
\][/tex]
This calculation gives us:
[tex]\[
\text{Ratio (as a percent)} = 0.445\%
\][/tex]
So, the ratio of the cash value to the premiums paid at the end of 10 years will be 0.445%.
To summarize:
- a. Tim will have paid \[tex]$20,000 in premiums over 10 years.
- b. The cash value of his policy at the end of 10 years will be \$[/tex]89.
- c. The ratio of cash value to premiums paid will be 0.445%.
