Answer:
[tex]t=24yrs[/tex]
Step-by-step explanation:
From the question we are told that:
Principle [tex]P=\$4000[/tex]
Interest [tex]r=5.5\%[/tex]
Final Value [tex]X=\$200000[/tex]
Generally the equation Time is mathematically given by
[tex]X=P *e^{r*t}\int^t_0 e^{r*t} dt[/tex]
[tex]200000=4000 *e^{0.055*t}\int^t_0 e^{0.055*t} dt[/tex]
[tex]200000=4000* \frac{e^{0.055*t}-1}{0.055}[/tex]
[tex]e^{0.055*t}=\frac{15}{4}[/tex]
[tex]e^{0.055*t}=3.75[/tex]
[tex]0.055t=ln3.75[/tex]
[tex]t=24.03[/tex]
Therefore the number of years it takes years for the account to be worth $200,000.
[tex]t=24yrs[/tex]
