Answer:
t=20.24 years
Step-by-step explanation:
-Continuous compounding happens over an infinite number of periods and is given by the formula:
[tex]A=Pe^{rt}[/tex]
Where:
- [tex]A[/tex] is the future value of the investment
- [tex]P[/tex] is the principal amount invested
- [tex]r,\ t[/tex] is the rate of interest and time respectively.
#We substitute the given values in the equation to solve for t:
[tex]A=2P\\\\\therefore 2P=Pe^{rt}\\\\2=e^{0.03425t}\\\\t=\frac{In \ 2}{0.03425}\\\\=20.237874\approx20.24\ years[/tex]
Hence, it takes approximately 20.24 years for the principal to double in value.
