Aprincipal amount of $600 is placed into a bank account compounded continuously at 3.5%. how long does it take for the amount to reach $1000?

For investments compounded continuously, we have



where P is the principal amount and A is the new amount after a period of time t.

Given the information that we have, we can solve for the time taken for the principal amount to reach $1000 as shown below.




For powers of e, we can use the natural logarithmic function, ln(). Recall that

 

Using what we know, we can solve for t in our equation. 






From this, we can see that it will take about 15 years for a principal amount of $600 to reach $1000 when compounded continuously at 3.5%.

15 years