Edward intends to retire in 20 years. Upon retirement, he will require a yearly

Question

Edward intends to retire in 20 years. Upon retirement, he will require a yearly cash flow of $70,000 for 25 years to support his lifestyle (yearly cash flows assumed to occur at the end of each year). Anticipating his retirement plan, he started investing $6,000 per year five years ago and will continue to do so for 20 more years. How much more (over the current level of $6,000 pa) will Edward have to invest each year for the next 20 years to have the necessary funds for his retirement? Use a 10% per year discount rate throughout this problem (for discounting or compounding).

Explanation / Answer

Formula for Present value of Annuity = PV= A*[(1+k)^n-1]/k*(1+k)^n A=70,000 per year n=25 years k =10% pa So The Present Value of Annuity after 20 years fro Edwards retirement cash flow will be   =70000*[(1.10)^25-1]/0.10*(1.10)^25 PV = $635,392.80 So the required retirement fund after 20 years = $635,392.80 The Future Value of $ 6000 annuity for   25 year will be = FV = A*[(1+k)^n-1]/k k=10% pa n =25 years FV = 6000*[(1.10)^25-1)/0.10= FV =590,082.40 So The future value of $6000 annuity after 20 years will be = $      590,082.4 Required fund value after 20 years = $      635,392.8 Shortfall amount   $      45,310.40 Assume yearly amt A has to be saved for 20 years to get the short fall amount; So A*[1.10^20-1]/0.10]=45310.40 A =$791.10 So Yearly $ 791.10 to be invested to reach the target   fund requirement after 20 years.

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