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Sagot :
To assess whether DeShawn made a wise decision selecting the [tex]$900,000 20-year term policy, let's analyze the details step-by-step:
1. Annual Premium for the 20-Year Term Policy:
- DeShawn's selected policy is a 20-year term life insurance policy.
- Given the annual premium per $[/tex]1,000 of face value is [tex]$15.38.
- For a face value of $[/tex]900,000:
[tex]\[ \text{Total Annual Premium} = \left(\frac{900,000}{1,000}\right) \times 15.38 = 900 \times 15.38 = 13,842 \][/tex]
- Therefore, the annual premium DeShawn has to pay is [tex]$13,842. 2. Total Cost Over the 20-Year Term: - Over the 20 years of the policy: \[ \text{Total Cost for 20-Year Term} = 13,842 \times 20 = 276,840 \] - So, the total cost DeShawn will pay over the 20 years is $[/tex]276,840.
3. Years Until Retirement:
- DeShawn is currently 38 years old and plans to retire at 60 years old:
[tex]\[ \text{Years Until Retirement} = 60 - 38 = 22 \][/tex]
- Hence, DeShawn has 22 years until retirement.
4. Comparison with 20-Year Endowment Policy:
- We calculate the annual premium for the 20-year endowment policy, given the premium rate per [tex]$1,000: \[ \text{Annual Premium for Endowment} = \left(\frac{900,000}{1,000}\right) \times 30.05 = 900 \times 30.05 = 27,045 \] - Total cost over the 20 years: \[ \text{Total Cost for 20-Year Endowment} = 27,045 \times 20 = 540,900 \] - Therefore, the total cost for the 20-year endowment policy would be $[/tex]540,900, which is significantly higher compared to the term policy.
5. Assessment of Adequacy and Coverage:
- The term policy covers DeShawn for 20 years, until he is 58 years old.
- His children, currently ages 2, 4, and 6, will be 22, 24, and 26 respectively at the end of this period, presumably independent.
- With his current salary of [tex]$45,000, the annual premium payments of $[/tex]13,842 are manageable.
Given the analysis:
- Option (a): DeShawn would be safer buying a whole life policy. Whole life policies are generally more expensive, and the provided premium rates indicate it is not cost-effective for DeShawn compared to the term policy.
- Option (b): DeShawn would have more money in the long run if he invested in the 20-year endowment. However, the endowment policy is more costly, $540,900 over 20 years, making it less financially advantageous compared to DeShawn's selected policy.
- Option (c): DeShawn's current policy will cover his family for an adequate period of time at his current salary. This option appears correct since the policy covers DeShawn until he is 58, which aligns with his retirement planning, and adequately supports his family until his children are independent.
- Option (d): DeShawn's current policy has too high of a face value and does not cover his family long enough. This is incorrect as the 20-year term provides sufficient coverage.
Conclusion: The best answer is (c). DeShawn's current policy will cover his family for an adequate period of time at his current salary.
[tex]\[ \text{Total Annual Premium} = \left(\frac{900,000}{1,000}\right) \times 15.38 = 900 \times 15.38 = 13,842 \][/tex]
- Therefore, the annual premium DeShawn has to pay is [tex]$13,842. 2. Total Cost Over the 20-Year Term: - Over the 20 years of the policy: \[ \text{Total Cost for 20-Year Term} = 13,842 \times 20 = 276,840 \] - So, the total cost DeShawn will pay over the 20 years is $[/tex]276,840.
3. Years Until Retirement:
- DeShawn is currently 38 years old and plans to retire at 60 years old:
[tex]\[ \text{Years Until Retirement} = 60 - 38 = 22 \][/tex]
- Hence, DeShawn has 22 years until retirement.
4. Comparison with 20-Year Endowment Policy:
- We calculate the annual premium for the 20-year endowment policy, given the premium rate per [tex]$1,000: \[ \text{Annual Premium for Endowment} = \left(\frac{900,000}{1,000}\right) \times 30.05 = 900 \times 30.05 = 27,045 \] - Total cost over the 20 years: \[ \text{Total Cost for 20-Year Endowment} = 27,045 \times 20 = 540,900 \] - Therefore, the total cost for the 20-year endowment policy would be $[/tex]540,900, which is significantly higher compared to the term policy.
5. Assessment of Adequacy and Coverage:
- The term policy covers DeShawn for 20 years, until he is 58 years old.
- His children, currently ages 2, 4, and 6, will be 22, 24, and 26 respectively at the end of this period, presumably independent.
- With his current salary of [tex]$45,000, the annual premium payments of $[/tex]13,842 are manageable.
Given the analysis:
- Option (a): DeShawn would be safer buying a whole life policy. Whole life policies are generally more expensive, and the provided premium rates indicate it is not cost-effective for DeShawn compared to the term policy.
- Option (b): DeShawn would have more money in the long run if he invested in the 20-year endowment. However, the endowment policy is more costly, $540,900 over 20 years, making it less financially advantageous compared to DeShawn's selected policy.
- Option (c): DeShawn's current policy will cover his family for an adequate period of time at his current salary. This option appears correct since the policy covers DeShawn until he is 58, which aligns with his retirement planning, and adequately supports his family until his children are independent.
- Option (d): DeShawn's current policy has too high of a face value and does not cover his family long enough. This is incorrect as the 20-year term provides sufficient coverage.
Conclusion: The best answer is (c). DeShawn's current policy will cover his family for an adequate period of time at his current salary.
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