Question

how long will it take for an investment to double in value if it earns 7.25 compounded continuously

Answer 1

The required formula is
\[A=Pe ^{rt}\]
P = principal
r = annual interest rate
t = number of years
A = amount after time t
Note: e is the base of natural logarithms

Answer 2

\[\frac{A}{P}=2=e ^{0.0725t}\]
Taking logs of both sides:
\[\ln 2=0.0725t\]
Now you just need to solve the last equation for t.