6000 is deposited into a fund at an annual interest rate of

$6000 is deposited into a fund at an annual interest rate of 13%. Algebraically, find the time required for the investment to double if the interest is compounded continuously.

Solution

A=P e^rt

Let after t years the amount gets doubled. And double of 6000 is 12000

12000= 6000 e^.13t

2= e^.13t

Taking ln on both sides

Ln 2/ .13=t

t=5.33 years