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Sagot :
To determine whether Eva made a wise decision, we need to compare the total cost of the 10-year term policy, the 20-year term policy, and the whole life policy over 20 years. Here is the detailed analysis:
1. Eva's chosen 10-year term policy:
- Eva chooses a [tex]$400,000 face value 10-year term policy. - The annual premium for a 10-year term policy for a female aged 29 is $[/tex]6.62 per [tex]$1,000 of face value. - Renewing after 10 years incurs an additional 40% charge. Calculating the annual premium for the first 10 years: \[ \text{Annual Premium (first 10 years)} = \left(\frac{\$[/tex]400,000}{\[tex]$1,000}\right) \times \$[/tex]6.62 = 400 \times \[tex]$6.62 = \$[/tex]2,648
\]
Calculating the annual premium for the next 10 years after the renewal:
[tex]\[ \text{Annual Premium (next 10 years)} = \$2,648 + 40\%\ (\$2,648) = \$2,648 + 0.4 \times \$2,648 = \$2,648 \times 1.4 = \$3,707.2 \][/tex]
Total cost over 20 years:
[tex]\[ \text{Total cost (first 10 years)} = \$2,648 \times 10 = \$26,480 \][/tex]
[tex]\[ \text{Total cost (next 10 years)} = \$3,707.2 \times 10 = \$37,072 \][/tex]
[tex]\[ \text{Total cost (10-year term policy over 20 years)} = \$26,480 + \$37,072 = \$63,552 \][/tex]
2. 20-year term policy:
- The annual premium for a 20-year term policy for a female aged 29 is [tex]$9.04 per $[/tex]1,000 of face value.
Calculating the annual premium:
[tex]\[ \text{Annual Premium} = \left(\frac{\$400,000}{\$1,000}\right) \times \$9.04 = 400 \times \$9.04 = \$3,616 \][/tex]
Total cost over 20 years:
[tex]\[ \text{Total cost (20-year term policy)} = \$3,616 \times 20 = \$72,320 \][/tex]
3. Whole life policy:
- The annual premium for a whole life policy for a female aged 29 is [tex]$18.63 per $[/tex]1,000 of face value.
Calculating the annual premium:
[tex]\[ \text{Annual Premium} = \left(\frac{\$400,000}{\$1,000}\right) \times \$18.63 = 400 \times \$18.63 = \$7,452 \][/tex]
Total cost over 20 years (note this policy continues beyond 20 years):
[tex]\[ \text{Total cost (whole life policy over 20 years)} = \$7,452 \times 20 = \$149,040 \][/tex]
Comparison:
- 10-year term policy total cost over 20 years: [tex]$63,552 - 20-year term policy total cost over 20 years: $[/tex]72,320
- Whole life policy total cost over 20 years: [tex]$149,040 Conclusion: Eva's decision to choose the 10-year term policy and then renew it for another 10 years results in the least expensive total cost over a 20-year period, which is $[/tex]63,552. Therefore:
Eva would have been better off selecting the 20-year term policy. (_Incorrect_)
Even with the extra charge for renewal, Eva's plan is the least expensive. (_Correct_)
Given that Eva plans to renew, she should have selected the whole life policy. (_Incorrect_)
Eva ends up paying the same amount for each policy. (_Incorrect_)
Thus, the best answer is:
Even with the extra charge for renewal, Eva's plan is the least expensive.
1. Eva's chosen 10-year term policy:
- Eva chooses a [tex]$400,000 face value 10-year term policy. - The annual premium for a 10-year term policy for a female aged 29 is $[/tex]6.62 per [tex]$1,000 of face value. - Renewing after 10 years incurs an additional 40% charge. Calculating the annual premium for the first 10 years: \[ \text{Annual Premium (first 10 years)} = \left(\frac{\$[/tex]400,000}{\[tex]$1,000}\right) \times \$[/tex]6.62 = 400 \times \[tex]$6.62 = \$[/tex]2,648
\]
Calculating the annual premium for the next 10 years after the renewal:
[tex]\[ \text{Annual Premium (next 10 years)} = \$2,648 + 40\%\ (\$2,648) = \$2,648 + 0.4 \times \$2,648 = \$2,648 \times 1.4 = \$3,707.2 \][/tex]
Total cost over 20 years:
[tex]\[ \text{Total cost (first 10 years)} = \$2,648 \times 10 = \$26,480 \][/tex]
[tex]\[ \text{Total cost (next 10 years)} = \$3,707.2 \times 10 = \$37,072 \][/tex]
[tex]\[ \text{Total cost (10-year term policy over 20 years)} = \$26,480 + \$37,072 = \$63,552 \][/tex]
2. 20-year term policy:
- The annual premium for a 20-year term policy for a female aged 29 is [tex]$9.04 per $[/tex]1,000 of face value.
Calculating the annual premium:
[tex]\[ \text{Annual Premium} = \left(\frac{\$400,000}{\$1,000}\right) \times \$9.04 = 400 \times \$9.04 = \$3,616 \][/tex]
Total cost over 20 years:
[tex]\[ \text{Total cost (20-year term policy)} = \$3,616 \times 20 = \$72,320 \][/tex]
3. Whole life policy:
- The annual premium for a whole life policy for a female aged 29 is [tex]$18.63 per $[/tex]1,000 of face value.
Calculating the annual premium:
[tex]\[ \text{Annual Premium} = \left(\frac{\$400,000}{\$1,000}\right) \times \$18.63 = 400 \times \$18.63 = \$7,452 \][/tex]
Total cost over 20 years (note this policy continues beyond 20 years):
[tex]\[ \text{Total cost (whole life policy over 20 years)} = \$7,452 \times 20 = \$149,040 \][/tex]
Comparison:
- 10-year term policy total cost over 20 years: [tex]$63,552 - 20-year term policy total cost over 20 years: $[/tex]72,320
- Whole life policy total cost over 20 years: [tex]$149,040 Conclusion: Eva's decision to choose the 10-year term policy and then renew it for another 10 years results in the least expensive total cost over a 20-year period, which is $[/tex]63,552. Therefore:
Eva would have been better off selecting the 20-year term policy. (_Incorrect_)
Even with the extra charge for renewal, Eva's plan is the least expensive. (_Correct_)
Given that Eva plans to renew, she should have selected the whole life policy. (_Incorrect_)
Eva ends up paying the same amount for each policy. (_Incorrect_)
Thus, the best answer is:
Even with the extra charge for renewal, Eva's plan is the least expensive.
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