Emily got a new job that guarantees her at 6% raise every year. if she started out making $25,000,how long will it be before she doubles her current salary?

Hello from MrBillDoesMath!

 about 12 years ( approx 11.9 years)

Discussion:

Salary at ...

end of year 1:  25000 + (.06) * 25000

end of year 2:  (salary at end of year 1) +

                                 .06(salary at end of year 1) =

                       (25000 + (.06)*25000) +

                 .06 (25000 + (.06)*25000)  

           The bold faced terms are the same. Factor out the boldfaced term to

           get

                     (25000 + .06*25000) ( 1 + .06)

            Factor 25000 out to get

                    25000 * (1 + .06) * (1+ .06)

            The last two terms multiple out to give (1 + .06)^2

            so

end of nth year salary is

           25000 * ( 1 + .06) ^n

To double her salary we need to find "n" such that

         50000 = 25000 ( 1.06) ^ n

Dividing both sides by 25000 gives

        2 = 1.06 ^n

Taking the logarithm of both sides gives:

log2 = n * log (1.06)   or

n = log2 / log(1/06)

This is approximately     0.3010 /  0.0253   or about 11.9 years.

Thank you,

MrB