Question

. You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 and your actuarial tables suggest that you will live to be 100. You want to move to the Bahamas when you retire. You estimate that it will cost you $ 300,000 to make the move (on your 65th birthday) and that your living expenses will be $30,000 a year (starting at the end of year 66 and continuing through the end of year 100) after that. a. How much will you need to have saved by your retirement date to be able to afford this course of action? b. You already have $50,000 in savings. If you can invest money, tax-free, at 8% a year, how much would you need to save each year for the next 30 years to be able to afford this retirement plan? c. If you did not have any current savings and do not expect to be able to start saving money for the next 5 years, how much would you have to set aside each year after that to be able to afford this retirement plan?

Answer 1

Solution a) Assume 5% cost of capital

Amount needed by the retirement date =300000+(30000/0.05)*(1-1/(1.05^35)) = $791,225.8

Solution b) PV of the cost at 8% rate is: =791225.8/(1.08^30) = 78,629.91

You already have 50 000, thus you need to save PV equal to 28,629.91 of through next 30 years

=78629.91-50000 = 28,629.91

Which means a year an annual saving of 2,542.121

= (28629.91*0.08)/(1-(1/1.08^30)) = $2,542.121

Solution c) The PV of the saving in terms of money in 5 years’ time is:

=791225.8/(1.08^25)=115,533.1

You will need to set aside 10,823 a year for the 25 years to be able to cover your spending:

=(115533.1*0.08)/(1-(1/1.08^25)) = $10,823

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