Question

If inflation is constant at 10% annually, in how many years will you be making 43,500$ per year?

Answer 1

In order to calculate how many years will take, let's use the formula for compound interest:

$A=P\cdot(1+i)^t$

Where A is the amount after t years, P is the principal (initial amount) and i is the annual interest rate.

So, using A = 43500, P = 34100 and i = 10% = 0.1, we have:

$\begin{gathered} 43500=34100\cdot(1+0.1)^t \\ 1.1^t=\frac{43500}{34100} \\ 1.1^t=1.27566 \\ \ln (1.1^t)=\ln (1.27566) \\ t\cdot\ln (1.1)=0.24346 \\ t\cdot0.09531=0.24346 \\ t=\frac{0.24346}{0.09531}=2.5544 \end{gathered}$

Rounding to the nearest whole year, we have an amount of time of 3 years.