Respuesta :
The SOLUTION
Recall the formula for compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]For the amount to double then A=2P
From the question it follows:
[tex]\begin{gathered} r=2\%=0.02 \\ n=4 \end{gathered}[/tex]Substituting these values gives:
[tex]2P=P(1+\frac{0.02}{4})^{4t}[/tex]Solve for t
[tex]\begin{gathered} 2=1.005^{4t} \\ \Rightarrow t\approx34.74 \end{gathered}[/tex]Therefore the number of years it will take for the amount to double is 34.74 years
Using the compounded continuously formula
Substituting values gives
[tex]2P=Pe^{0.02t}[/tex]Solve for t
[tex]\begin{gathered} 2=e^{0.02t} \\ \Rightarrow t\approx34.66 \end{gathered}[/tex]For compounded continuously, the investment will double in about 34.66 years
