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 capital needs / annuity method. Calculate how much capital Steven will need.

Steven will need a capital of $1,061,342.10

Explanation:

Annual Savings

= $80,000*0.8

= $64,000.00

Period

= 68 - 43

= 25  

Future Value of annual savings

= FV

= $64000*(1 + 0.03)^25

= $134,001.79

Future Value of social security

= FV

= $26000*(1 + 0.03)^25

= $54,438.23

Annual Investment required at age of 68

= $134,001.79 - $54,438.23

= $79,563.56  

Present value of a number of cash flows over his retirement years,

Inflation Adjusted Rate

= (1.08/1.03) - 1

= 4.85%  

Period

= 90 - 68

= 22  

Capital Required

= PV(4.85%,22,-79563.56)

= $1,061,342.10  

Therefore, Steven will need a capital of $1,061,342.10