Assume that your brother is now 50 years old, that he plans to retire in 10 year
ID: 2616169 • Letter: A
Question
Assume that your brother is now 50 years old, that he plans to retire in 10 years and that he expects to live for 25 years after he retires (until he is 85 years old). He wants a fixed retirement income that has the same purchasing power at the time he retires as $50,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin pm the day after he retires, 10 years from today, and he will then get 24 additional annual payments Inflation is expected to be 3% per year from today forward. Your brother currently has a savings of $275,000 and expects to earn a return on his savings of 8% per year, annual compounding. To the nearest dollar, how much must your brother save during each of the next 10 years (with deposits being made at the end of each year) in order to meet his retirement goal? PLEASE calculate in excel using appropriate excel formulas to showing how you arrived at your answer
Explanation / Answer
Soln : He wants an income 0f $50000, equivalentt o the present value, yearly from the day he retired.
Let's calculate the value he required = 50000*(1.03)10 = 67196
So, he will be having 25 installments yearly of this amount, starting at his retirement.
Please refer the table tota; present value of 25 installments, he received at age of 65
Now. let x be the amount he need to save yearly for getting this amount.
We can say that the 10 years savings value at age of 65 should equal to the value calculated above
Or
X*(F/A, 8%, 10) = 774686.44
X * ((1.08)10 -1 )/0.08 = 774686.44
On solving we get X = 53476
Brother should save $53476 yearly to get the retirement fund as required by him.
Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Income 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 67196 Discount rate @8% 1 0.93 0.86 0.79 0.74 0.68 0.63 0.58 0.54 0.50 0.46 0.43 0.40 0.37 0.34 0.32 0.29 0.27 0.25 0.23 0.21 0.20 0.18 0.17 0.16 PV 67196 62218.52 57609.74 53342.35 49391.07 45732.47 42344.88 39208.22 36303.91 33614.73 31124.75 28819.21 26684.46 24707.83 22877.62 21182.98 19613.87 18160.99 16815.73 15570.12 14416.78 13348.87 12360.07 11444.51 10596.76 NPV 774686.44 0