\(1.015^{n}(4000) = 1.04^{n}(3542)\)
Divide both sides by 4000.
\(1.015^{n} = 1.04^{n}(\frac{3542}{4000})\)
Divide both sides by 1.04^n
\(\frac{1.015^{n}}{1.04^{n}}=\frac{3542}{4000}\)
That is:
\((\frac{1.015}{1.04})^{n}=\frac{3542}{4000}\)
\((\frac{1.015}{1.04})^{n}=0.8855\)
n equals the log base (1.015/1.04) of 0.8855, but since most calculators can only do base 10 or base e, we will need to use a change of base formula.
This page talks about the change of base formula: http://www.purplemath.com/modules/logrules5.htm
That tells you that:
n = [ln 0.8855]/[ln (1.015/1.04)]
Just plug that into a calculator to get that
n ≈ 4.998
