Question

Annual sales for a company are $375,000 and they increase at a rate of 7% each year. Find the company’s sales after 6 years.

Answer 1

Notice that 7%=7/100=0.07

After the first year, the annual sales are

$375000+0.07(375000)=375000(1+0.07)$

After the second year,

$\begin{gathered} (375000+0.07(375000))+0.07(375000+0.07(375000))=(1+0.07)(375000+0.07(375000)) \\ =(1+0.07)^2375000 \end{gathered}$

Therefore, in general, after n years, the annual sales are

$f(n)=375000(1+0.07)^n$

Set n=6; then,

$\begin{gathered} f(6)=375000(1.07)^6=562773.881943375 \\ \Rightarrow f(6)\approx562773.88 \end{gathered}$

The answer is approximately $562773.88, the exact answer is $562773.881943375