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# Pension funds

A company sets up a pension fund for its employees. Its aim is to pay out £1,500 monthly to each pensioner over his / her remaining lifetime. The actuary assumes that employees retire at the age of 65 and have a life expectancy of 20 more years after that. The company wishes to set aside a certain amount of money P for each pensioner such that the pension payments can be fully funded out of the interest earned on P and by using up the capital P over the remaining expected lifetime of each pensioner (i.e., the company wants to have paid out P to the pensioner over the 20 year horizon). The actuary believes that the company can achieve a 6% annual return over the 20 year horizon.

a. How much money does the company need to have set aside for each employee when they retire?
b. A new study suggests that life expectancy has increased by 5 years. Calculate by how much the pension fund is underfunded if this prediction is correct? Similarly, what is the amount of underfunding if the company only manages to earn 5% annually on its investment?