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Because Aaron, age 32, is a smoker, he must pay more for life insurance. Given that Company A charges 20% more for smokers, Company B charges 18% more for smokers, Company C charges 25% more for smokers, and Company D charges 15% more for smokers, Aaron decides to buy his $250,000 policy from Company B. Which of the following statements is true?




\multirow[t]{3}{*}{Age}		\multicolumn{4}{|l|}{Annual Insurance Premiums (per $1,000 of face value)}

\multicolumn{4}{|l|}{10-Year Term}

Company ACompany BCompany CCompany D

30		1.301.291.401.49

31		1.572.522.641.55

32		1.861.862.072.25





AAaron is paying the smallest premium possible with Company B.
BAaron is paying $93 more in premiums than he would with Company A.
CAaron is paying $129 more in premiums than he would with Company C.
DAaron could have chosen any company because the premiums are all the same.

Verified Answer :

  • The total annual premium is calculated by multiplying the base rate by 250 and applying the specific smoker surcharge for each company: Company A: \(\$558.00\), Company B: \(\$548.70\), Company C: \(\$646.88\), and Company D: \(\$646.88\).
  • Comparing these costs, Company B offers the lowest annual premium among all options.
  • Checking the provided statements, the only true statement is that Aaron is paying the smallest premium possible by choosing Company B.
  • Final Answer: \(\boxed{\text{a}}\)

Explanation

  1. Analyzing the Data

We need to evaluate which statement is true for Aaron, a 32-year-old smoker purchasing a \$250,000 life insurance policy. The base annual premiums for a 32-year-old (per \$1,000 of face value) are: Company A: \$1.86, Company B: \$1.86, Company C: \$2.07, and Company D: \$2.25. The face value of \$250,000 implies a multiplier of \(\frac{250,000}{1,000} = 250\). Each company imposes a smoker surcharge on the base premium: Company A: 20%, Company B: 18%, Company C: 25%, and Company D: 15%.,number:1,title:

  1. Calculating Premiums

We calculate the total annual premium for each company by multiplying the base rate by 250 and then applying the smoker surcharge.

  • For Company A: \(\text{Premium}_A = 1.86 \times 250 \times (1 + 0.20) = 465 \times 1.20 = \$558.00\).
  • For Company B: \(\text{Premium}_B = 1.86 \times 250 \times (1 + 0.18) = 465 \times 1.18 = \$548.70\).
  • For Company C: \(\text{Premium}_C = 2.07 \times 250 \times (1 + 0.25) = 517.5 \times 1.25 = \$646.875\), which we round to \(\$646.88\).
  • For Company D: \(\text{Premium}_D = 2.25 \times 250 \times (1 + 0.15) = 562.5 \times 1.15 = \$646.875\), which we round to \(\$646.88\).,number:2,title:
  1. Comparing Results and Conclusion

We compare the calculated annual premiums:

  • \(\text{Premium}_A = \$558.00\)
  • \(\text{Premium}_B = \$548.70\)
  • \(\text{Premium}_C = \$646.88\)
  • \(\text{Premium}_D = \$646.88\)

Comparing these values, \(\$548.70\) is the smallest premium. Therefore, Aaron has chosen the company that offers the lowest annual premium among those listed. Let's verify the other statements:

  • Statement a: Aaron is paying the smallest premium, which is true.
  • Statement b: Aaron is paying \(\$548.70 - \$558.00 = -\$9.30\) (he is paying less, not more).
  • Statement c: Aaron is paying \(\$548.70 - \$646.88 = -\$98.18\) (he is paying less, not more).
  • Statement d: Premiums are clearly not all the same.,number:3,title:

Examples

When shopping for insurance, it is essential to calculate the total cost rather than just looking at the base rate. Many factors, such as age, health habits like smoking, and the specific terms of the policy, significantly impact the final price. By calculating the total annual premium for each potential provider using the formula \(\text{Total Premium} = \text{Base Rate} \times \text{Face Value Multiplier} \times (1 + \text{Surcharge})\), you can make an informed financial decision and secure the most cost-effective protection for your needs.

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