Answer :
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.
### 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.
