Answer
(a) It would take 11.55 years for an investment to double in value.
(b) The equivalent annual interest rate is 6.18%
Work Step by Step
(a) $A(t) = A_0e^{rt}$
$A_0e^{0.06~t} = 2A_0$
$e^{0.06~t} = 2$
$0.06~t = ln~2$
$t = \frac{ln~2}{0.06}$
$t = 11.55~years$
It would take 11.55 years for an investment to double in value.
(b) We can find the value after one year:
$A(t) = A_0e^{rt}$
$A(1) = A_0e^{(0.06)(1)}$
$A(1) = 1.0618~A_0$
The equivalent annual interest rate is 6.18%
