Question

Jordan, age 46, currently makes $143,000. She expects that inflation will average 2.75 percent for her entire life expectancy. She expects to earn 8.5 percent on her investments and retire at age 65 and live to age 92. She has sent for and received her Social Security benefit statement, which indicated that her Social Security retirement benefit in today’s dollars adjusted for early retirement is $20,000 per year. It is reasonable to subtract the Social Security benefit from today’s needs because it is inflation adjusted.

Calculate the amount of capital Jordan will need at retirement according to the purchasing power preservation model.

Answer 1

Net amount Needed (Yearly) = 143000-20000 = $123,000

Calculation of Yearly amount needed at retirement (after inflation) :

t = 65-46 = 19

Inflation(I) = 2.75%

Money needed at the age of 65 = 123000*1.0275¹⁹ = $ 205,949.10

Calculation for capital required by jordan at the time of retirement :

Inflation adjusted Real rate = (1.085/1.0275) - 1   = 0.055961 or 5.5961%

Assumption :- We are considering that Jordan will require the yearly amount from the Start of retirement till her Death. It means she will requirement 27 payment at the start of every year.

So,

Present value of Annuity = P + P*[1-(1+r)^-n]/r      

                                                                                               Where, (1+r)^-n = 1/(1+r)ⁿ

                                                                                                            n = 27-1 = 26

                                                                                                            First P = Payment of first year at the start

                                                                                                           Second P = yearly Payment of next 26 years

                                                                                                                       r = 0.055961

Present value of Annuity = 205949.10 + 205949.10*[1-(1+0.055961)^-26 ]/0.055961

Present value of annuity = 205949.10 + 205949.10*13.53179

Present value of annuity = 29,92,809.07

So, Total capital required needed at the age of retirement = $2,992,809.07 or $2,992,809