Question

1. Jordan wants to retire in 15 years when he turns 65. Jordan wants to have enough money to replace 75% of his current pre-tax (before income tax and FICA) income in annual installments at the beginning of each year less what he expects to receive from Social Security. He expects to receive $20,000 per year from Social Security in today's dollars. Jordan is conservative and wants to assume a 6% annual investment rate of return and to assume that inflation will be 4% per year. Based on his family history, Jordan expects that he will live to be 95 years old. Jordan currently has no assets set aside for retirement. If Jordan currently earns $100,000 per year and he expects his raises to equal the inflation rate and his income in retirement to increase at the inflation rate, approximately how much does he need at reetirement to fulfill his retirement goals? Hint: Beginning as $1,268,887. b. $2,242,055. c. $2,285,172. d. $3,057,348.

I need assistance with this question.

Answer 1

Annual Salary after 15 years (at the time of retirement) with 4% (inflation rate) increase every year =

= 100000 * (1+4%)^15 =  180094.350550692

Social Security receivable in 16th year = 20000 * (1+4%)^16 = 37459.6249145439

Amount Jordan Expects in first Year (16th year from now)= 180094.350550692 * (1+inflation rate) * 75% = 140473.59342954

Amount Jordan Needs in first year = 140473.59342954 - 37459.6249145439 = 103013.968514996

Money Jordan needs at retirement is equal to present value of annuity of 103013.968514996, growing at the rate of inflation (4%), which pays interest at the rate of 6% for 30 years.

Present value of growing annuity = [P / (r-g)] * [1- {(1+g)/(1+r)}^n] where

P = First Payment = 103013.968514996

r = interest rate = 6%

g = annuity growth rate = 4%

n = number of years = 30

Amount Jordan Needs at retirement = [103013.968514996 / (6%-4%)] * [1- {(1+4%)/(1+6%)}^30]

= [103013.968514996 / 2%] * [1- (0.981132075471698)^30]

= 5150698.4257498 * 0.43529163493388

= 2242055.94

Summary:

Question: Approximately how much does Jordan needs at retirement

Answer: b. $2,242,055