Answer: t ≈ 20 years
Step-by-step explanation:
Since it is compounded continuously , we will use the compound interest formula:
A = P[tex]e^{rt}[/tex]
Where A is the amount when tripled
P is the initial amount
r is the rate
t is the time
since the investment is tripled , it means the A = 3P.
From the question:
A = 3P
P = $6000
r = 5.5%
t = ?
Substituting into the formula , we have
3P = P[tex]e^{rt}[/tex] , that is
3(6000) = 6000[tex]e^{0.055t}[/tex]
Dividing through by 6000 , we have
3 = [tex]e^{0.055t}[/tex]
Take the In of both sides in order to remove the exponential , that is
In 3 = 0.055t
divide through by 0.055
t = In 3 / 0.055
Therefore :
t = 19.97476888
t≈ 20 years
