A 45 year old woman is considering taking out a funeral plan insurance policy with InsurCo. The premium is $2.72 per week, with payments commencing the week after she takes out the policy. Upon her health, his family will receive a payout of $6000. A friend suggests that an alternative approach to funeral plan insurance is simply to establish a savings account and deposit the $2.72 into the savings account each week. Providing this is set up as joint account, her family could withdraw her accumulated savings upon her death. The friend suggests a savings account at the Friendly Bank, which pays interest at tax adjusted rate of j52=1.56%p.a.

According to the Australian Bureau of Statistic, the life expectancy of a 45 year old woman is 87, (that is, another 42 years.)

a) Assuming that the woman lives another 42 years, illustrate the cash flows associated with the saving account option a fully labelled time line diagram.

b) Assuming that she lives to her life expectancy, determine the amount she will accumulate with the saving account option. Thus comment on whether savings account option or the funeral plan insurance represents the best value, for this scenario.

c) Determine the minimum time she needs to live in order for the savings account to be the better option.

d) Describe and perform a quick sanity check on your answer from part c).

e) Determine the equivalent interest rate, j52, that this funeral insurance policy delivers for a 45 year old woman who exactly reaches her life expectancy. [That is, what j52 would be required for 2184 week annuity of $2.72 per week to have a future value of $6000. Iterate until you find an I that gives a FV within 1 cent of $6000.00. Show your working for at least three iterations.] Then proceed to find the effective annual rate, j1.