Question

At the end of this month, Leslie will start saving $200 a
month for retirement through his company's superannuation plan. His
employer will contribute an additional $0.50 for every $1.00 that
he saves. He is employed by this firm for 30 more years and earns
an average of 11% monthly compounding on his retirement savings.
Required:

a. How much will Leslie have in his superannuation account 30
years from now?

b. If at the end of year 20, Leslie voluntarily puts $20 000
in his superannuation, how much will he has in that account when he
retires?

c. Leslie has a second investment and it will start to pay him
$ 25,000 next year and after that the payment will grow at 4% each
year for the rest of his life. How much is the present value of
Leslie’s investment payments if the required rate of returns is
8%?

d. How much is the present value of this second investment
cash flow if the payment is the same every year and the rate of
return is the same 8%?

Answer #1

a) Total monthly contribution = 200 + 50% x 200 = 300

Future Value canbe calculated using FV function on a calculator

N = 30 x 12 = 360, PMT = 300, I/Y = 11%/12, PV = 0

=> Compute FV = $841,355.92

b) FV of that contribution can be calculated as follows

N = 10 x 12 = 120, I/Y = 11%/12, PMT = 0, PV = 20,000

=> Compute FV = $59,782.99

Hence, total value = $901,138.91

c) Present value of growing perpetuity can be calculated as follows

PV = CF1 / (r - g) = 25,000 / (8% - 4%) = $625,000

d) If g = 0% in c => PV = $312,500

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