Question

Marcus makes an investment of $2000 that increases in value by 8% per year.
How many years will it take for him to have $5000. Round to the nearest year.

Answer 1

Answer: 12 years

Step-by-step explanation:

Let 's use the compound interest formula :

$\rm \displaystyle S=A\left( 1+\frac{N}{100} \right)^{\rm \big r}$

Where N- the percentage by which we raise the price ; r-years ; A-the original price

In our case

N=8%  ;  r=?  ; A=5000$  

And we know :

$\rm \displaystyle S= 5000 \\\\ 2000 \left( 1+ \frac{8}{100} \right)^{\big {r}}=5000 \\\\(1,08)^{\big r} = 2,5 \\\\ r= \log_{1,08}\ 2,5 =11,\underline9059 \approx12 \ years$