Mr. Suresh, aged 55, purchases a life annuity policy from Life Insurance Corporation of India by investing à·¹8,00,000. The policy provides an annual payment of à·¹75,000 at the end of each year as long as he survives. The annual effective interest rate is 5%.
The probabilities that Mr. Suresh survives for the next 4 years are given below:
<t****/td>
| Year | Survival Probability |
|---|---|
| 0.97 | |
| 2 | 0.94 |
| 3 | 0.90 |
| 4 | 0.85 |
At the same time, he also purchases a life insurance policy with a sum assured of à·¹12,00,000. The probability of death within one year is 0.03.
The present value of the annuity payments is given by:
PV=\sum_{t=1}^{4}\frac{75000\times p_t}{(1.05)^t}
and the expected insurance claim is:
E(X)=1200000\times0.03
Questions
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Calculate the expected present value of the life annuity.
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Find the expected insurance claim amount.
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Determine whether the annuity investment is beneficial for Mr. Suresh.
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Explain the role of probability in contingent payments and life insurance.