Suppose sallys annual salary increased each year such that i

Suppose sally\'s annual salary increased each year such that if double every 15 years she worked she work at age 20 and

Solution

Given : salary doubled every 15 yrs:

S(t) = Soe^(kt)

where So is the intial salary and k is salary growth factor , t is no. of years

So, 2So = Soe^(15k)

2 = e^15k

take natural log on both sides:

ln(2) = 15k

k = ln(2)/15 = 0.046

At what age was she making half the salary that she got at retirement.

Salary at the age of retirement Soe^45k = Soe^(45*0.046) = 7.92So

S(t) = 7.82So/2 = 3.96So

3.96So = Soe^(0.046t)

3.96 = e^(0.046t)

take natural log on both sides:

ln(3.96)/0.046 = t

t = 29.91 years

Age = 20 +29.91 = 50 years