3. Maria inherits a portfolio of the following investments. It is currently 2016

Question

3. Maria inherits a portfolio of the following investments. It is currently 2016, and she expects to retire in 2056. Maria's MARR is 10%. Calculate the (future) worth of each investment at the time of Maria's retirement in 2056. a. Investment W pays $1,000 in 2046. In 2056, investment w is worth (5 marks) b. Investment x pays $100 in 2058, and this yearly payment increases by $100 each year (so it pays $200 in 2059, $300 in 2060, etc.). The final payment is in 2068. In 2056, investment X is worth (5 marks) c. Investment Y pays $100 in 2017, after which this yearly payment increases by 10% each year (soit pays $100 in 2017, $110 in 2018, $121 in 2019, etc.). The final payment is in 2056. (5 marks In 2056, investment Y is worth

Explanation / Answer

a) Calculation of future worth of investment : year Investment Compounding worth in pays Return each yr. 2046 $1,000.00 $100.00 $1,100.00 2047 $1,100.00 $110.00 $1,210.00 2048 $1,210.00 $121.00 $1,331.00 2049 $1,331.00 $133.10 $1,464.10 2050 $1,464.10 $146.41 $1,610.51 2051 $1,610.51 $161.05 $1,771.56 2052 $1,771.56 $177.16 $1,948.72 2053 $1,948.72 $194.87 $2,143.59 2054 $2,143.59 $214.36 $2,357.95 2055 $2,357.95 $235.79 $2,593.74 2056 $2,593.74 $259.37 $2,853.12 In 2056, investment W is worth $ 2,853.12 b) calculation of present value of investment of future cash flows : year Cash flow PVAnnuity factor Present @ 10% value 2056 0 1 0.00 2057 0 0.909 0.00 2058 $100 0.826 $82.60 2059 $200 0.751 $150.20 2060 $300 0.683 $204.90 2061 $400 0.621 $248.40 2062 $500 0.564 $282.00 2063 $600 0.513 $307.80 2064 $700 0.466 $326.20 2065 $800 0.424 $339.20 2066 $900 0.385 $346.50 2067 $1,000 0.350 $350.00 2068 $1,100 0.319 $350.90 In 2056, investment X is worth $1,531.44 c) calculation of future value of Y investment : rate of interest 10% no. Of pyments 40 amount of payment 100 based on the above data, investment Y is worth $4,724.23 Note: annual interest rate is divided by 12 because it is compounded monthly.

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