Question

Class, if you have a pension that will kick in 15 years from now and pay you $4,000 per month for 20 years, what is the present value of this pension if the appropriate discount rate to use is 6%? Show your work.

This example is based on a pilot of Delta airlines that lost his pension during the airline's bankruptcy a few years back.

Answer 1

Monthly Payment = $4,000
Annual Interest Rate = 6%
Monthly Interest Rate = 6%/12 = 0.5%

Value of Pension after 15 years = $4,000/1.005 + $4,000/1.005^2 + $4,000/1.005^3 + … + $4,000/1.005^240
Value of Pension after 15 years = $4,000 * (1 - (1/1.005)^240) / 0.005
Value of Pension after 15 years = $4,000 * 139.58077
Value of Pension after 15 years = $558,323.08

Present Value of Pension = $558,323.08/1.005^180
Present Value of Pension = $227,506.84

So, present value of this pension is $227,506.84