Question

John Roberts is offered an incentive package if he retires after 5 years. After retirement, the incentive package will pay him an additional $20,000 at the end of each year for the following 20 years. Assume that the relevant interest rate is 12%, compounded annually, how much is the incentive package worth today?

Answer 1

This problem will let understand the time value of money

$1 is worth more today than in future due to interest factor.

Step 1 :

first we will find the value at the time of retirement(5 years from now) of $20,000 received every year for 20 years .

rate = 12%

present value annuity n =20 r = 12%

[1+1.12]¹+[1+1.12]²...........[1+1.12]²⁰

⁼7.469

present value of 20000$ received every year for 20 years =20000*7.469

=$149,380 is the value after 5 years

Step 2:

so we will now find today's value

present value factor[1/1.12]⁵ = 0.568

incentive package worth today = 149,380*0.568

=$84,847.84