Question

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?

Answer 1

Answer

After 12 years  Emily's  salary will be doubled

Explanation

Here the salary increase can be considered as increase in the principle amount annually.  

There are two methods to calculate the number of years.

1) 72 Rule

The rule state that, the number of years required to double the principle amount at given rate of interest, we just divide 72 by the interest rate.

In this problem Principle amount =$25,000 (in this rule no importance in principle amount)

Rate of interest, R = 6%

Number of years taken to double the amount = 72/6 =12 years

2)compound interest calculation method

P[1+R/100]^N = 2P

[1+ R/100 ]^N= 2

R is 6%, N is number of years

(1.06)^N =2

e^(ln(1.06^N)) = 2

e^N㏒(1.06)=2

N x ㏑(1.06) = ㏑(2)

N =㏑(2)/㏑(1.06) ≈11.8917 ≈ 12 years