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

rate = 11%

Time (n) = 28

FV = 6000*((1+11%)^{2}^{8}-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

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Discuss in case of doubt

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