Question

# You are trying to decide how much to save for retirement. Assume you plan to save...

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)

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%

Best of Luck. God Bless
Discuss in case of doubt

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