Colin is 40 years old and wants to retire in 27 years. His family has a history
ID: 2815298 • Letter: C
Question
Colin is 40 years old and wants to retire in 27 years. His family has a history of living well into their 90s. Therefore, he estimates that he will live to age 95. He currently has a salary of $150,000 and expects that he will need about 85% of that amount annually at the beginning of each year if he were retired. He can earn 8.5% from his portfolio and expects inflation to continue at 3%. Some years ago, he worked for the government and expects to receive an annuity from his pension plan that will pay him $20,000 in today’s dollars per year beginning at age 67. The annuity includes a cost of living adjustment equal to inflation. Colin currently has $200,000 invested for his retirement. His Social Security benefit in today’s dollars is $30,000 per year at his normal age retirement of age 67. Approximately how much does he need to accumulate in his investment portfolio by age 67 to meet his retirement income needs, assuming he does not wish to leave a financial legacy for his heirs (round to the nearest $100,000)?
Explanation / Answer
Now we need to calculate present value of growing perpetuity by given formula
Now the pv of funds = 167136* [1- {(1+0.03)/(1+0.085)}29 / (8.5% - 3%)
= 167136 * ( 1 - 0.221218)/5.5% = 2366592
Funds already have = 200000
the value of the amount at the time of retirement = 200000*(1+0.085)27 = 1809810
Therefore funds required are = 2366592 - 1809810 = 556781 is answer
Feel free to ask any query
Solution :- The PV of the amount that is paid after retirement age of 67 PV of the future amount Withdrwl amount 150000*85% 127500 Less:- Cover form govt. Pension -20000 Less : - Cover from social security -30000 Net amount needed 77500 After inflation = 77500(1+0.03)26 167136 Interest rate = 8.5% life = 29 years