Question

It is important for Bob to have a gross salary in his fifth year of at least $100,000. He is promised salary increases of 3 percent per year in the second and third years and 5 percent thereafter. What must be his starting salary be to achieve his goal? My original answer was $87,000, but I think $86,000 might work. All of the percents are running together in my head. I think I will go get a Coke. Thanks in advance for your help.

Answer 1

salary in 1st year --- x
salary in 3rd year = x(1.03)^2
salary in 4th year = x(1.03)^2 (1.05)
salary in 5th year = x(1.03)^2 (1.05)^2

x(1.03)^2 (1.05)^2 = 100000
x = 100000/((1.03)^2 (1.05)^2)
= $87,180.84

Answer 2

WOW! Thanks, I had trouble setting up the equation to solve. But it makes sense, like when solving an interest problem.