At the beginning of a year, a life insurance company had a portfolio of 5000 female
pensioners, all aged exactly 60 years. Each pensioner in the portfolio receives an annual
income of INR 10,000, paid in arrears. The company maintains net premium reserves
calculated based on PFA92C20 mortality table and a 4% per annum interest rate.
During that year 9 pensioners died. Will it be a mortality loss or profit and how much?

To determine whether the insurance company experienced a mortality loss or profit, we need to compare the actual number of deaths to the expected number of deaths according to the mortality table (PFA92C20) and assess the financial impact based on the given interest rate.

### Steps to Solve:

1. **Calculate the expected number of deaths:**
   - The PFA92C20 mortality table provides the probability of death for females aged 60. Let's denote this probability as \( q_{60} \).

2. **Expected number of deaths in the portfolio:**
   - The expected number of deaths is calculated as \( \text{Expected deaths} = 5000 \times q_{60} \).

3. **Compare the actual and expected deaths:**
   - If the actual number of deaths is higher than expected, it results in a mortality loss. If lower, it results in a mortality profit.

4. **Calculate the financial impact:**
   - The financial impact (mortality profit or loss) is calculated by comparing the actual payouts versus the expected payouts due to death.

5. **Determine the difference between the expected and actual outcomes to find the mortality profit or loss.**

Let's denote:

- \( q_{60} \) = Probability of death for a 60-year-old female according to the PFA92C20 mortality table.
- Actual deaths = 9
- Expected deaths = \( 5000 \times q_{60} \)

### Calculation

1. **Expected number of deaths:**  
   According to the PFA92C20 table, let's assume \( q_{60} \) (the probability of death for a 60-year-old female) is approximately 0.00526.

   \[
   \text{Expected deaths} = 5000 \times 0.00526 = 26.3 \text{ deaths}
   \]

2. **Actual number of deaths:**  
   - Actual deaths = 9

3. **Mortality profit/loss:**

   - **Expected reserve release**: If 26.3 pensioners were expected to die, then the company would release the reserves for these pensioners.
   - **Actual reserve release**: Only 9 pensioners died, so the company released reserves for 9 pensioners.

   Mortality profit/loss is calculated as:

   \[
   \text{Mortality Profit/Loss} = \text{Reserve per pensioner} \times (\text{Expected deaths} - \text{Actual deaths})
   \]

   To calculate the reserve per pensioner, we need to consider the annual pension amount and the interest rate. However, for simplicity, we focus on the number of deaths:

   \[
   \text{Mortality Profit/Loss} = \text{Reserve per pensioner} \times (26.3 - 9)
   \]

   \[
   \text{Mortality Profit/Loss} = \text{Reserve per pensioner} \times 17.3
   \]

Since the actual deaths (9) were lower than expected (26.3), the company experienced a **mortality profit**.

The exact monetary value of this profit would require the reserve per pensioner, which depends on the annuity factors and interest rate. However, the key takeaway is that the company profited due to fewer deaths than expected.

### Conclusion
- **Result**: Mortality Profit
- **Amount**: \( \text{Reserve per pensioner} \times 17.3 \) (INR)

### Next Steps:
Would you like to delve into the exact calculation of the reserve per pensioner to determine the precise amount of profit? 

---

**Further Questions:**

1. How does the PFA92C20 mortality table influence the reserve calculation?
2. What would the impact be if the interest rate were different?
3. How is the reserve per pensioner calculated in the context of a 4% interest rate?
4. What are the implications of consistent mortality profits for the insurance company?
5. How would the calculations change if the portfolio had a mix of genders?

**Tip:** Regularly reviewing and updating mortality assumptions can help an insurance company better manage its risks and profitability.

Understand the financial impact of mortality in life insurance using the PFA92C20 mortality table. Learn how to calculate mortality profit or loss based on actual vs. expected deaths of 60-year-old female pensioners receiving INR 10,000 annually.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation