Question

1. You are given
   1. An individual age 75 buys a 4 year endowment insurance.
   2. The insured will receive $500 at the end of year of death if they die during the term, or $1200 if they survive the term.
   3. q_x = 0.05 for all t,x
   4. Level annual premiums of P are paid at the beginning of each year, for the first two years, while the insured is alive
   5. i = 3%

Calculate the annual premium P.

Answer 1

Answer:

for all x,t

Expected Present Value of Benefits = Expected Present Value of Premium

So, Let annual premium be P

Expected Present value of Premium

  

  ............equation (1)

Expected Present Value of Benefits

= Expected Present Value of Benefits payable on Death + Expected Present Value of Benefits payable on Survival

.........equation (2)

EPV of Premium = EPV of Benefits {using equation (1) and (2)}

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