We have to use the compount interest formula
[tex]\begin{gathered} A=P(1+r)^t \\ \frac{A}{P}=(1+r)^t \\ \\ \sqrt[t]{\frac{A}{P}}=\sqrt[t]{(1+r)^t}^ \\ \\ r=\sqrt[t]{\frac{A}{P}}\text{ - }1 \\ \\ r=\sqrt[21]{\frac{5000}{2000}}\text{ - }1 \\ r=0.04459 \\ r=4.45\%=4.5\% \end{gathered}[/tex]
A is the total amount
P is the principal amount
r is the interest annual rate, which is the unknown variable and t is the nnumber of yeaers
That would be the formula for the r. Let's find it then
For a the annual rate of interest is 4.5%
2) Now, we have the r, we can find the number 2 which is how long for it to double, so we have to find t.
[tex]\begin{gathered} A=P(1+r)^t \\ \\ 4000=2000(1+0.045)^t \\ \\ \frac{4000}{2000}=(1.045)^t \\ 2=1.045^t \\ \log_{1.045}2=t \\ \\ t=15.747=15.75\text{ years} \end{gathered}[/tex]
So, for it to double it takes 15.75 years.
