Advanced Time Value of Money Problems
(Try to work this question WITHOUT using Excel, get calculationin detail)
Question (Retirement planning)
You have just graduated Hofstra University at age 22. You hardwork has paid off as you already have a job as an investment bankerat Goldman Sachs waiting for you. You plan to work continuouslyuntil age 65 and retire exactly on that day. You expect to liveuntil exactly 90 and enjoy your golden years and leave you heirsNOTHING. Assume your investments earn 8% per year.
You plan to contribute $10,000 to your retirement fund everyyear on your birthday starting at age 23. Your last deposit will beat exactly age 65 and your first withdrawal will be at age 66. Yourlast withdrawal will be at the moment you die at age 90.
Ignore all tax considerations for this problem.
(i) How much you will be able to spend each year in retirement?
(ii)
FV (deposits) = PV (withdrawals)
NOTE: This could be at any time period but t=65 is particularlyconvenient
How much will you be able to spend each year in retirement ifyou begin deposits at age 30?
(iii) How much larger do your deposits have to be if depositsstart at age 30 to equal your answer in part (i)?
Now let’s consider the effect of inflation.
The values calculated above are nominal values. However, what ismore important is real, i.e. inflation-adjusted, values.
Assume inflation averages 4% per year.
(iv) Re-calculate parts (i), (ii) and (iii) above.
(v) Comment on above.
