To determine whether Eva made a wise decision by choosing a 10-year term policy, we need to evaluate and compare the total costs associated with each policy option over 20 years. Here are the relevant details from the given information:
1. Eva is currently paying an annual premium rate of [tex]$7.84 for the 10-year term policy.
2. The premium rate for the 20-year term policy is $[/tex]10.40 annually.
3. The premium rate for a whole life policy is [tex]$20.05 annually.
4. After the initial 10-year term ends, the insurance company will charge an extra 40% to renew Eva's premium rate for the next 10 years.
Let's break down the total costs for these policies over the 20-year period.
### 1. 10-Year Term Policy (with renewal after 10 years)
- Initial 10 years:
\[
10 \text{ years} \times \$[/tex]7.84 \text{ per year} = \[tex]$78.40
\]
- Renewal cost for the next 10 years (with an extra 40% charge):
\[
\text{Renewal premium rate} = \$[/tex]7.84 \times 1.4 = \[tex]$10.976 \text{ per year}
\]
\[
10 \text{ years} \times \$[/tex]10.976 \text{ per year} = \[tex]$109.76
\]
- Total cost for 20 years:
\[
\$[/tex]78.40 + \[tex]$109.76 = \$[/tex]188.16
\]
### 2. 20-Year Term Policy
- Total cost for 20 years:
[tex]\[
20 \text{ years} \times \$10.40 \text{ per year} = \$208.00
\][/tex]
### 3. Whole Life Policy
- Total cost for 20 years:
[tex]\[
20 \text{ years} \times \$20.05 \text{ per year} = \$401.00
\][/tex]
Now, let's evaluate the provided options based on these costs:
a. Eva would have been better off selecting the 20-year term policy:
[tex]\[
\$208.00 \text{ (20-year term policy)} > \$188.16 \text{ (10-year term with renewal)}
\][/tex]
This is false because the 10-year term policy with renewal is less expensive.
b. Even with the extra charge for renewal, Eva's plan is the least expensive:
Comparing all the totals:
[tex]\[
\$188.16 \text{ (10-year term with renewal)} < \$208.00 \text{ (20-year term policy)} < \$401.00 \text{ (whole life policy)}
\][/tex]
This is true as the 10-year term policy with renewal is indeed the least expensive.
c. Given that Eva plans to renew, she should have selected the whole life policy:
[tex]\[
\$401.00 \text{ (whole life policy)} > \$188.16 \text{ (10-year term with renewal)}
\][/tex]
This is false because the whole life policy is more expensive.
d. Eva ends up paying the same amount for each policy:
[tex]\[
\$188.16 \neq \$208.00 \neq \$401.00
\][/tex]
This is false as the costs for each policy are different.
Therefore, Option b is the correct assessment:
b. Even with the extra charge for renewal, Eva's plan is the least expensive.
