An individual decides to start saving for retirement. They want to purchase an annuity of $4,000 per month starting at age 65. Assume mortality follows the SULT and = 5%, and apply the Woolhouse formula in 3 terms as required. a) Assume they purchase this policy at age 45. 

a) What is the monthly premium payable from age 45 to retirement as calculated by the equivalence principle? 

b) Assume instead that they purchase this policy at age 25. What is the monthly premium payable from age 25 to retirement as calculated by the equivalence principle? 

c) Explain in words why the magnitude of change in premiums is greater than the magnitude of change in the number of premiums, and what the implications of this would be on an educated investor?