Question

You are 22 and plan to work for 43 years until you retire at 65. You expect to live until you are 88.

You will collect a pension. Your annual pension payment will be equal to your final salary times a 3% crediting rate times the number of years that you work.

Your starting salary (paid at the end of the year) is $50,000. You expect to get a 4% annual raise.

Your discount rate is 5%.

Draw a timeline and Identify:

• Annual salary payment

• Time of retirement

• Annual pension payment

• Value of pension at retirement

• Value of pension today

Answer 1

Annual salary at the time of retirement i.e. 43 years = Today’s salary *(1+Annual raise%)^{No of years}

                                                 = 50000*(1+4%)⁴³

                                                          = 50000*5.4005

                                                = $270025

Pension payment = Final salary * (1+(3%*43))

                 = 270025*(1+(3%*43))

                 = $618357.25

Pension value at retirement = PV value of all future pension payments

Using excel function we can get PV and fv values

PV = PV( rate, nper, pmt, fv)

Here

Rate = 5%

Nper = 88-65 = 23

Pmt=$618357.25

Fv=0

PV =pv(5%,23,-618357.25,0)

     = $8,340,757.45

Present value today = $8,340,757.45/1.05^43

                     = $1,023,447.65