To determine the cash value of Susan Williams' whole life insurance policy at specific anniversary dates, let's break down the given information and follow through the calculations as described:
### Given Information:
- Policy Amount: \[tex]$80,000
- Cash Value at 5 years: \$[/tex]2,400
- Cash Value at 20 years: \[tex]$18,560
### Step-by-Step Solution:
1. Calculate the Cash Value Rate at 5 Years:
- The cash value of the policy at 5 years is given as \$[/tex]2,400.
- To find the cash value rate, we use the formula:
[tex]\[
\text{Cash Value Rate} = \frac{\text{Cash Value at } 5 \text{ years}}{\text{Policy Amount}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Cash Value Rate at 5 Years} = \frac{2400}{80000}
\][/tex]
So, the cash value rate at 5 years is:
[tex]\[
0.03 \text{ or } 3\%
\][/tex]
2. Calculate the Cash Value at 5 Years:
- Using the policy amount and the cash value rate calculated:
[tex]\[
\text{Cash Value} = \text{Policy Amount} \times \text{Cash Value Rate}
\][/tex]
Substituting the values:
[tex]\[
\text{Cash Value at 5 Years} = 80000 \times 0.03 = 2400
\][/tex]
- This confirms that the cash value at 5 years is indeed \[tex]$2,400.
3. Calculate the Cash Value Rate at 20 Years:
- The cash value of the policy at 20 years is given as \$[/tex]18,560.
- To find the cash value rate, we use the same formula:
[tex]\[
\text{Cash Value Rate} = \frac{\text{Cash Value at } 20 \text{ years}}{\text{Policy Amount}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Cash Value Rate at 20 Years} = \frac{18560}{80000}
\][/tex]
So, the cash value rate at 20 years is:
[tex]\[
0.232 \text{ or } 23.2\%
\][/tex]
4. Calculate the Cash Value at 20 Years:
- Using the policy amount and the cash value rate calculated:
[tex]\[
\text{Cash Value} = \text{Policy Amount} \times \text{Cash Value Rate}
\][/tex]
Substituting the values:
[tex]\[
\text{Cash Value at 20 Years} = 80000 \times 0.232 = 18560
\][/tex]
- This confirms that the cash value at 20 years is indeed \[tex]$18,560.
### Summary:
- The cash value of Susan Williams' \$[/tex]80,000 whole life insurance policy at 5 years is \[tex]$2,400.
- The cash value of the policy at 20 years is \$[/tex]18,560.
These calculations verify the provided cash values at the specific anniversary dates using the cash value rates derived from the given information.
