"Steven, age 43, earns $80,000 annually; and his wage replacement ratio has been determined to be 80%. He expects inflation will average 3% for his entire life expectancy. He expects to work until 68, and live until 90. He anticipates an 8% return on his investments. Additionally, Social Security Administration has notified him that his annual retirement benefit, in today s dollars will be $26,000. Using the purchasing power preservation model, calculate how much capital Steven needs, in order to retire at 68. "

Explanation:

Savings Per Month- 80% of $80,000 = $ 64,000.

 Future value for the Yearly saving of $64,000 and Social security of $26,000 for balance years of 25 (68-43)

Future Value= Present value (1+rate of interest)n

Future Value =64,000(1+0.03)∧25= 134,001.7875

Future value= $26,000(1+0.03)∧25- 54,438.22617

Difference= 1,340,001.7875 - 54,438.22617 =  $79,563.56133

present value of a number of cash flows for 22 years after his retirement i.e. 90-68.. The Net rate is 5% i.e. (8%-5%)

Present Value= C   1−(1+r)−n                                                                                                                                                                                                                                                                                                                                                                                             r

                 =$79,563.56   (1−(1+.05)−22                                                                                                                                                                                                                                                                                                                                                                                              0.05

Present value =$1,047,295.35

So he needs capital of $ 1,047,295.35 in order to retire at 68