Maria, age 28, wants to pay no more than $300 a year in life insurance. What is the face value of the largest 20-year term policy she can buy without spending more than $300 annually?
| Age | Annual Insurance Premiums (per $1,000 of face value) |
|---|---|---|---|---|
| | 10-Year Term | 15-Year Term | 20-Year Term | Whole Life |
| | Female | Female | Female | Female |
| 28 | 1.28 | 1.54 | 1.89 | 9.46 |
A. $234,000
B. $158,000
C. $11,000
D. $567,000
Answer (1)
Define x as the face value of the policy in thousands of dollars.
Set up the inequality 1.89 x ≤ 300 .
Solve for x : x ≤ 1.89 300 ≈ 158.73 .
Calculate the face value: 158.73 × 1000 = 158730 , round down to $158 , 000 . The final answer is $158 , 000 .
Explanation
Problem Analysis Maria, who is 28 years old, wants to purchase a 20-year term life insurance policy. She wants to pay no more than $300 per year. The insurance premium for a 20-year term policy for a 28-year-old female is $1.89 per $1,000 of face value. We need to find the largest face value of the policy she can buy without exceeding her budget.
Setting up the Inequality Let x be the face value of the policy in thousands of dollars. The annual premium for the policy is 1.89 x . We need to find the largest x such that 1.89 x ≤ 300 .
Solving for x To find the maximum face value, we solve the inequality 1.89 x ≤ 300 for x . Dividing both sides by 1.89 , we get: x ≤ 1.89 300 ≈ 158.73
Calculating the Face Value Since x represents the face value in thousands of dollars, the largest face value Maria can buy is approximately $158.73 \times 1000 = $158,730. Since Maria cannot exceed $300, we round down to the nearest dollar, which is $158,000.
Selecting the Best Answer Comparing the result with the given options: a. $234 , 000 b. $158 , 000 c. $11 , 000 d. $567 , 000 The closest and largest affordable option is $158 , 000 .
Final Answer Therefore, the largest 20-year term policy Maria can buy without spending more than $300 annually is $158 , 000 .
Examples
Life insurance helps protect your loved ones financially in case of an unexpected event. For example, if Maria were to pass away during the 20-year term, her beneficiaries would receive $158 , 000 . This money could be used to cover funeral expenses, pay off debts, or provide ongoing financial support. Understanding how to calculate the maximum coverage you can afford helps you make informed decisions about protecting your family's future.
