Solution: We know that formula for continuously compound interest is:
[tex] A= P e^{rt} [/tex]
Where A is the future amount $900 x 2 = $1800
P is the principal investment $900
e is the eular's constant
r is rate of interest 0.09
t is the time ( to be found)
Therefore we have:
[tex] 1800=900 \times e^{0.09 \times t} [/tex]
[tex] 2=e^{0.09 \times t} [/tex]
Taking natural log on both sides
[tex] ln(2)=0.09 \times t [/tex]
[tex] t=\frac{ln(2}{0.09} [/tex]
[tex] t=7.702 [/tex]
Therefore it will take 7.702 years to double the amount
