Homework 3 - document contains solution for mgec assignment PDF

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Problem 3 An annuity provides insurance against out-living one’s financial resources. LEICO, a life insurance company, takes a deposit from customers at age 60 years, and returns an annual payment of Rs. 5000 till their death. (a) Calculate the break-even deposit for LEICO if average population-wide...

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Problem 3 An annuity provides insurance against out-living one’s financial resources. LEICO, a life insurance company, takes a deposit from customers at age 60 years, and returns an annual payment of Rs. 5000 till their death. (a) Calculate the break-even deposit for LEICO if average population-wide life expectancy is 80 years. Assume a 5% interest rate. (b) If potential customers have a sense of their life expectancy, based on factors such as the longevity of their parents, who will purchase the annuity with the deposit you have calculated above? (c) If c (up to a maximum of 100 years) and potential customers have a sense of their life expectancy, what is the deposit that LEICO will ultimately end up charging? Who will finally buy this annuity? 3. a. LEICO takes a deposit at age 60 and pays ₹ 5000 for each deposit Given average life expectancy is 80 years and interest rate (r) = 5% Given value of each payment P = 5000 And Number of periods (n) = 20 Present Value = P*(1- (1+r)^-n)/r Hence PV = 5000*(1-(1+0.05)^-20)/0.05 = ₹ 62,311 In order for LEICO to break even the amount of deposit should be equal to the total present value of future payments i.e the Deposit = ₹ 62,311 b. If potential customers have an estimate of their life expectancy, they might decide whether to go for the plan or not based on the average life expectancy the plan is built around. Customers will prefer to go for the plan if their life expectancy is more than the annuity’s life expectancy of 80 years so as to maximize their return on deposit. If customers expect a lower life expectancy than 80 years they might not be able to fully realize the value of their deposit as the payment will stop once they pass away. c. Let size of the population be n = 100. Deposit is paid at 60 years which is the minimum expectancy And given maximum life expectancy is 100 years As life expectancy is uniformly distributed in the population the average life expectancy will be an arithmetic mean (60+100)/2 = 80 Now, people who are above 80 years of age will enrol to the annuity to obtain the maximum benefit on their investment. Hence the new average age of the customers will be (80+100)/2 = 90 years The Present value of the Annuity can be found out using PV = P*(1- (1+r)^-n)/r Given interest rate (r) = 5% Given value of each payment P = 5000

And Number of periods (n) = 30 (90 yrs. – 60 yrs) Hence PV = 5000*(1-(1+0.05)^-30)/0.05 = ₹ 76,862.2551...