Question

if you make 51000.00 and are promised a 5% raise every year how much will you make in 5 years?

Answer 1

we can look at this as

you go to a bank, deposit 51000, and they promise you a bump annually of 5% in interest.

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 51000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=51000\left(1+\frac{0.05}{1}\right)^{1\cdot 5}\implies A=51000(1.05)^5\implies A = 65090.3596875$

just to point out, that's how much your bumped up salary is 5 years later.