Peter And Marcia, Both Age 34, Can Each Pay $650 A Year For Life Insurance. About How Much Is The Face Value Of The Largest Combination Of Policies They Can Buy? [ \begin{array}{|c|c|c|} \hline \text{Age} & \text{Annual Insurance Premiums (per
Introduction
When it comes to purchasing life insurance policies, individuals often face a dilemma: how much can they afford to spend on premiums while still ensuring that their loved ones are protected in the event of their passing? In this article, we will explore the concept of combining life insurance policies and use mathematical calculations to determine the face value of the largest combination of policies that Peter and Marcia can buy.
Understanding Life Insurance Policies
Life insurance policies are designed to provide a financial safety net for beneficiaries in the event of the policyholder's death. The face value of a life insurance policy is the amount of money that will be paid out to the beneficiary upon the policyholder's passing. In this scenario, Peter and Marcia are both 34 years old and can each pay $650 per year for life insurance.
The Problem
Given that Peter and Marcia can each pay $650 per year for life insurance, we need to determine the face value of the largest combination of policies they can buy. To do this, we will use a mathematical approach to find the maximum face value of the policies.
Mathematical Formulation
Let's assume that Peter and Marcia each purchase a life insurance policy with a face value of $x. The annual premium for each policy is $650. We can represent the total cost of the policies as a function of the face value:
Total Cost = 2 * (Annual Premium * Number of Policies)
Since Peter and Marcia each purchase one policy, the total cost is:
Total Cost = 2 * ($650 * 1)
Total Cost = $1300
However, this is not the only factor that determines the face value of the policies. We also need to consider the fact that the policies are for life, meaning that the face value will be paid out only once, upon the policyholder's passing. To account for this, we can use the concept of present value, which represents the current value of a future payment.
Present Value
The present value of a future payment can be calculated using the formula:
Present Value = Future Value / (1 + r)^n
where:
- Future Value is the amount of the payment
- r is the interest rate
- n is the number of years until the payment is made
In this case, the future value is the face value of the policy, and the interest rate is the annual premium. Since the policies are for life, we can assume that the interest rate is 0, and the number of years is infinite.
Calculating the Face Value
Using the present value formula, we can calculate the face value of the policies as follows:
Face Value = Total Cost / (1 + 0)^∞
Face Value = Total Cost
Face Value = $1300
However, this is not the maximum face value that Peter and Marcia can buy. We need to consider the fact that they can each pay $650 per year for life insurance, which means that they can each purchase a policy with a face value of $650 * 100 = $65,000.
The Largest Combination of Policies
To find the largest combination of policies that Peter and Marcia can buy, we need to consider the fact that they can each purchase a policy with a face value of $65,000. Since they can each pay $650 per year for life insurance, the total cost of the policies is:
Total Cost = 2 * ($650 * 100)
Total Cost = $130,000
However, this is not the only factor that determines the face value of the policies. We also need to consider the fact that the policies are for life, meaning that the face value will be paid out only once, upon the policyholder's passing. To account for this, we can use the concept of present value, which represents the current value of a future payment.
Present Value (Revisited)
Using the present value formula, we can calculate the face value of the policies as follows:
Face Value = Total Cost / (1 + 0)^∞
Face Value = Total Cost
Face Value = $130,000
However, this is not the maximum face value that Peter and Marcia can buy. We need to consider the fact that they can each pay $650 per year for life insurance, which means that they can each purchase a policy with a face value of $650 * 100 = $65,000.
The Final Answer
Based on the calculations above, the face value of the largest combination of policies that Peter and Marcia can buy is:
$130,000
This is the maximum face value that they can purchase, given that they can each pay $650 per year for life insurance.
Conclusion
Q: What is the main goal of combining life insurance policies?
A: The main goal of combining life insurance policies is to determine the maximum face value of the policies that Peter and Marcia can buy, given that they can each pay $650 per year for life insurance.
Q: How do you calculate the face value of a life insurance policy?
A: The face value of a life insurance policy is calculated by multiplying the annual premium by the number of years until the policyholder's passing. In this case, since the policies are for life, we can assume that the number of years is infinite.
Q: What is the present value of a future payment?
A: The present value of a future payment is the current value of a future payment, calculated using the formula: Present Value = Future Value / (1 + r)^n, where r is the interest rate and n is the number of years until the payment is made.
Q: How do you calculate the present value of a life insurance policy?
A: To calculate the present value of a life insurance policy, we can use the formula: Present Value = Future Value / (1 + 0)^∞, since the policies are for life and the interest rate is 0.
Q: What is the total cost of the policies?
A: The total cost of the policies is calculated by multiplying the annual premium by the number of policies, which is 2 in this case. The total cost is $1300.
Q: What is the maximum face value of the policies that Peter and Marcia can buy?
A: Based on the calculations above, the maximum face value of the policies that Peter and Marcia can buy is $130,000.
Q: What are some common mistakes to avoid when combining life insurance policies?
A: Some common mistakes to avoid when combining life insurance policies include:
- Not considering the present value of the policies
- Not accounting for the fact that the policies are for life
- Not calculating the total cost of the policies correctly
Q: How can I determine the maximum face value of the policies that I can buy?
A: To determine the maximum face value of the policies that you can buy, you should:
- Calculate the total cost of the policies
- Consider the present value of the policies
- Account for the fact that the policies are for life
- Use the formula: Face Value = Total Cost / (1 + 0)^∞ to calculate the face value of the policies
Q: What are some benefits of combining life insurance policies?
A: Some benefits of combining life insurance policies include:
- Increasing the face value of the policies
- Reducing the total cost of the policies
- Providing a financial safety net for beneficiaries in the event of the policyholder's passing
Q: What are some limitations of combining life insurance policies?
A: Some limitations of combining life insurance policies include:
- The policies must be for life
- The policies must have the same annual premium
- The policies must have the same number of years until the policyholder's passing
Conclusion
In this article, we answered some frequently asked questions about combining life insurance policies. We covered topics such as calculating the face value of a life insurance policy, the present value of a future payment, and the total cost of the policies. We also discussed some common mistakes to avoid and some benefits and limitations of combining life insurance policies.