Answer :
Maria wants to find the face value of the largest 20-year term life insurance policy she can buy without spending more than \[tex]$300 annually. For her age (28), the annual insurance premium per \$[/tex]1,000 of face value for a 20-year term policy is \[tex]$1.59.
Let's break down the calculation step-by-step:
1. Annual budget for the insurance:
\[\$[/tex]300\]
2. Annual premium per \[tex]$1,000 of face value: \[\$[/tex]1.59\]
3. To find the maximum face value that can be afforded with the given budget:
First, calculate the number of thousands of dollars of face value that \[tex]$300 can cover. \[ \text{Number of thousands of dollars} = \frac{\$[/tex]300}{\[tex]$1.59} \] 4. Perform the division: \[ \frac{300}{1.59} \approx 188.67 \] 5. Convert this number to actual dollars: Since the number we calculated represents thousands of dollars: \[ \text{Face value} = 188.67 \times 1000 \approx 188,679.25 \] Thus, the face value of the largest 20-year term policy Maria can buy without spending more than \$[/tex]300 annually is approximately \[tex]$188,679. Therefore, none of the given multiple-choice options exactly match the calculated face value. However, since the true calculated answer is approximately \$[/tex]188,679, let's verify that none of the given options (\[tex]$234,000, \$[/tex]158,000, \[tex]$11,000, \$[/tex]567,000) are closer to the calculated value.
The closest answer should match within reasonable rounding differences, but none do. Given the precise calculation, the correct face value based on our calculation is approximately:
[tex]\[ \$188,679.25 \][/tex]
2. Annual premium per \[tex]$1,000 of face value: \[\$[/tex]1.59\]
3. To find the maximum face value that can be afforded with the given budget:
First, calculate the number of thousands of dollars of face value that \[tex]$300 can cover. \[ \text{Number of thousands of dollars} = \frac{\$[/tex]300}{\[tex]$1.59} \] 4. Perform the division: \[ \frac{300}{1.59} \approx 188.67 \] 5. Convert this number to actual dollars: Since the number we calculated represents thousands of dollars: \[ \text{Face value} = 188.67 \times 1000 \approx 188,679.25 \] Thus, the face value of the largest 20-year term policy Maria can buy without spending more than \$[/tex]300 annually is approximately \[tex]$188,679. Therefore, none of the given multiple-choice options exactly match the calculated face value. However, since the true calculated answer is approximately \$[/tex]188,679, let's verify that none of the given options (\[tex]$234,000, \$[/tex]158,000, \[tex]$11,000, \$[/tex]567,000) are closer to the calculated value.
The closest answer should match within reasonable rounding differences, but none do. Given the precise calculation, the correct face value based on our calculation is approximately:
[tex]\[ \$188,679.25 \][/tex]
