To determine the face value of the largest 20-year term policy that Maria can buy without exceeding her annual budget of \[tex]$300, follow these steps:
1. Identify the relevant annual premium per $[/tex]1,000 of face value: For a 20-year term policy and a 28-year-old female, the annual premium is \[tex]$1.59 per $[/tex]1,000 of face value.
2. Set up the equation: The maximum annual payment Maria wants to make is \[tex]$300. Therefore, the relationship between the face value of the policy and the annual premium can be expressed as:
\[
\text{Annual Payment} = \left(\frac{\text{Face Value}}{1000}\right) \times \text{Annual Premium per \$[/tex]1000}
\]
Substitute the given values into the equation:
[tex]\[
300 = \left(\frac{\text{Face Value}}{1000}\right) \times 1.59
\][/tex]
3. Solve for the face value:
[tex]\[
\frac{\text{Face Value}}{1000} = \frac{300}{1.59}
\][/tex]
[tex]\[
\text{Face Value} = \frac{300}{1.59} \times 1000
\][/tex]
[tex]\[
\text{Face Value} \approx 188679.24528301888
\][/tex]
Hence, the face value of the largest policy Maria can buy without spending more than \[tex]$300 annually is approximately $[/tex]\[tex]$188,679. This value matches the calculation closely, which means \( \$[/tex]188,679 \) is the correct answer.
Now let's review the choices provided:
a. \[tex]$234,000
b. \$[/tex]158,000
c. \[tex]$11,000
d. \$[/tex]567,000
The closest value to our calculated figure of approximately \[tex]$188,679 is not exactly listed, but option \( b. \, \$[/tex]158,000 \) seems to be the conservative choice that would definitely not exceed the budget. Nevertheless, our precise and accurate answer, as calculated, is actually very close to \[tex]$188,679.
So, despite none of the options fitting perfectly, the best answer from the closest approximation is:
a. \$[/tex]188,679 (but given none existing, closest one is not listed).
