Using Table 3.1:

1.What is the probability that a man aged 50 dies within 4 years?

2.Calculate the minimum annual premium an insurance company should charge for a $1 million four-year term insurance contract issued to a 50-year-old man. Assume that the premium is paid at the beginning of each year, that death claims for each year are paid at the end of the year, and that the risk free rate is 2% per annum (compounded semiannually).

3.Repeat question b for a 4-year endowment to this man. This contract again pays $1 million on death during the first four years, but if the man survives the 4-year period the contract pays $1 million at t=4.

Table 3.1 Mortality Table Male Female Probability Probability Age of Death Survival Life of Death Survival Life (Years) within 1 Probability Expectancy within 1 Probability Expectancy Year Year 0 0.006519 1.00000 76.28 0.005377 1.00000 81.05 0.000462 0.99348 75.78 0.000379 0.99462 80.49 2 0.000291 0.99302 74.82 0.000221 0.99425 79.52 3 0.000209 0.99273 73.84 0.000162 0.99403 78.54