(part a)

Assume that a pension plan offers to pay $300,000 on a persons retirement (his/her sixty-fifth birthday) or a semi-annual annuity for the remainder of the persons life i.e., starting 6 months from the date of retirement and including his/her date of death. Interest rates are 8 per cent compounded semi-annually, and a persons life expectancy has been determined statistically as being 80 years. Calculate the amount of the annuity that would make a person indifferent between the options?

(part b)

A person joins a pension plan at age 35. How much will s/he have to pay into the pension fund each year in order to accumulate a balance of $250,000 by the time s/he retires (age 65)? Assume that the payments start on his/her 35 birthday and the final payment is on his/her 60 the birthday. Interest rates are 7% compounded annually

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