Question

You are trying to decide how much to save for retirement. Assume you plan to save $8,000 per year with the first investment made one year from now. You think you can earn 5.5​%

per year on your investments and you plan to retire in 32 ​years, immediately after making your last $8,000 investment.

a. How much will you have in your retirement account on the day you​ retire?

b.​ If, instead of investing $8,000 per​ year, you wanted to make one​ lump-sum investment today for your retirement that will result in the same retirement​ saving, how much would that lump sum need to​ be?

c. If you hope to live for 19 years in​ retirement, how much can you withdraw every year in retirement​ (starting one year after​ retirement) so that you will just exhaust your savings with the 19th withdrawal​ (assume your savings will continue to earn 5.5​% in​ retirement)?

d.​ If, instead, you decide to withdraw $132,000 per year in retirement​ (again with the first withdrawal one year after​ retiring), how many years will it take until you exhaust your​ savings? (Use​ trial-and-error, a financial​ calculator: solve for​ "N", or​ Excel: function​ NPER)

e. Assuming the most you can afford to save is $1,600 per​ year, but you want to retire with $1,000,000 in your investment​ account, how high of a return do you need to earn on your​ investments? (Use​ trial-and-error, a financial​ calculator: solve for the interest​ rate, or​ Excel: function​ RATE)

Answer 1

a) Annual Saving = 8000, Arte 5.5%, No of periods=32

You need to calculate how much you hace after 32 yer ai.e. future value of all you savings.

Put value in finacial calculator(texas ba 2) as N=32, I/R= 5.5, PV=0, PMT=8000 compute FV = 661419.98

So you will have 661,420 Approx after 32 years.

b) Instead of 8000, Lumpsump payment to get 614420 value.

You need to do dicounting and bring back 661420, 32 years.Like

= 119,233.59 is Lumpsum amount required to invest.

c) To live 19 year in retirement, Need to calculate annual withdrals to exhaust amount 661420.

Put value in financial calculator as N=19, I/Y=5.5, PV= 661420, FV=0 Compute PMT = 56981.37

Annual withdrawl required= 56981.37

d) Now witdraw 132000 annual, How many year it took to exhaust 661420.

Put values = I/Y= 5.5, PV= 661420, PMT= - 132000, FV=0, Compute N= 6.022 years.

e) Annual Saving= 1600, Years = 32, Amount required = 1000000 Calculate Rate

Put values as N=32, PV=0, PMT= -1600, FV = 1000000 compute I/Y = 15.37%

15.37% rate of interest required.