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Sagot :
To determine the best life insurance policy for Alphonso, we need to compare the different aspects of each option, particularly focusing on the cost-effectiveness and the protection period.
### Breakdown of Policies
Policy A:
- Type: Term
- Death Benefit: [tex]$200,000 - Protection Period: 15 years - Cost per Year: $[/tex]495
Policy B:
- Type: Term
- Death Benefit: [tex]$200,000 - Protection Period: 30 years - Cost per Year: $[/tex]500
Policy C:
- Type: Whole
- Death Benefit: [tex]$200,000 - Protection Period: Life - Cost per Year: $[/tex]6900
Policy D:
- Type: Whole
- Death Benefit: [tex]$200,000 - Protection Period: Life - Cost per Year: $[/tex]7100
### Step-by-Step Calculation and Comparison
1. Calculate the Cost Effectiveness:
- For Policy A, the cost per year of protection is calculated by dividing the annual cost by the number of years of protection:
[tex]\[ \text{Cost effectiveness of Policy A} = \frac{\$495}{15 \text{ years}} = \$33 \text{ per year of protection} \][/tex]
- For Policy B, the cost per year of protection is:
[tex]\[ \text{Cost effectiveness of Policy B} = \frac{\$500}{30 \text{ years}} = 16.\overline{6} \text{ per year of protection} \][/tex]
2. Comparing Cost-Effectiveness:
- Policy A has a cost effectiveness of [tex]$33 per year of protection. - Policy B has a cost effectiveness of approximately $[/tex]16.67 per year of protection.
Based on these calculations, Policy B is more cost-effective than Policy A.
3. Comparison with Whole Life Policies:
- Policy C and Policy D offer lifetime protection, but they cost significantly more annually ([tex]$6900 and $[/tex]7100, respectively).
- Since we are looking for minimization of cost while ensuring significant protection, Term policies offer a better balance of cost to coverage compared to Whole life policies.
4. Final Decision:
- Both Policy C and Policy D are more expensive annually compared to Policy A and Policy B.
- Between the term policies, Policy B provides a lower cost per year of protection and also offers twice the term length (30 years) compared to Policy A (15 years).
In conclusion, considering cost-effectiveness and duration of protection, Policy B is the best option for Alphonso. It has the lowest cost-per-year of protection and offers protection for a longer period of time.
So, the best life insurance policy for Alphonso is Policy B.
### Breakdown of Policies
Policy A:
- Type: Term
- Death Benefit: [tex]$200,000 - Protection Period: 15 years - Cost per Year: $[/tex]495
Policy B:
- Type: Term
- Death Benefit: [tex]$200,000 - Protection Period: 30 years - Cost per Year: $[/tex]500
Policy C:
- Type: Whole
- Death Benefit: [tex]$200,000 - Protection Period: Life - Cost per Year: $[/tex]6900
Policy D:
- Type: Whole
- Death Benefit: [tex]$200,000 - Protection Period: Life - Cost per Year: $[/tex]7100
### Step-by-Step Calculation and Comparison
1. Calculate the Cost Effectiveness:
- For Policy A, the cost per year of protection is calculated by dividing the annual cost by the number of years of protection:
[tex]\[ \text{Cost effectiveness of Policy A} = \frac{\$495}{15 \text{ years}} = \$33 \text{ per year of protection} \][/tex]
- For Policy B, the cost per year of protection is:
[tex]\[ \text{Cost effectiveness of Policy B} = \frac{\$500}{30 \text{ years}} = 16.\overline{6} \text{ per year of protection} \][/tex]
2. Comparing Cost-Effectiveness:
- Policy A has a cost effectiveness of [tex]$33 per year of protection. - Policy B has a cost effectiveness of approximately $[/tex]16.67 per year of protection.
Based on these calculations, Policy B is more cost-effective than Policy A.
3. Comparison with Whole Life Policies:
- Policy C and Policy D offer lifetime protection, but they cost significantly more annually ([tex]$6900 and $[/tex]7100, respectively).
- Since we are looking for minimization of cost while ensuring significant protection, Term policies offer a better balance of cost to coverage compared to Whole life policies.
4. Final Decision:
- Both Policy C and Policy D are more expensive annually compared to Policy A and Policy B.
- Between the term policies, Policy B provides a lower cost per year of protection and also offers twice the term length (30 years) compared to Policy A (15 years).
In conclusion, considering cost-effectiveness and duration of protection, Policy B is the best option for Alphonso. It has the lowest cost-per-year of protection and offers protection for a longer period of time.
So, the best life insurance policy for Alphonso is Policy B.
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