Question

You are trying to decide how much to save for retirement. Assume you plan to save $6,000 per year with the first investment made one year from now. You think you can earn 11.0​% per year on your investments and you plan to retire in 28 ​years, immediately after making your last $6,000 investment.

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

b.​ If, instead of investing $6,000 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 26 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 26th withdrawal​ (assume your savings will continue to earn 11.0​% in​ retirement)?

d.​ If, instead, you decide to withdraw $192,000 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 $1,200 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

1 a) Savings = 6000
rate = 11%
Time (n) = 28
FV = 6000*((1+11%)²⁸-1)/11% = 958,903.72

b) Lump sum * ( 1+11%)²⁸ =958,903.72
Lumpsum = 51609.73

c)Let Amount of withdrwal = PMT
Number of year n =26
958,903.72= PMT*(1- (1+r)^-n/r
958,903.72 = PMT*(1 -(1+11%)^-26/11%
PMT = 112,970..92

d) Retirement account = 958,903.72
Using excel function = NPER(11%,192000,-958,903.72) = 7.64 years

e) Savings = 1200
FV = 1,000,000
Number of years =28
Rate using excel function = Rate(28,-1200,0,1000000) = 20.09%

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