How many years will it take $8,000 to grow to $14,400 if it is invested at 3.50% compounded​ continuously?

Question

How many years will it take $8,000 to grow to $14,400 if it is invested at 3.50% compounded​ continuously?

Answer 1

When finding future value that the interest compound continuously, we use the fomular below:

Future value = Present Value x e^rate x time period

But future value = 14400

Present value = 8000

Rate = 3.5%

Time period = ?

Therefore the time period is solved using the calculator as e^(0.035t)= 14400/8000 and press solve

And time will be give as 16.79390471 approximately 17 years.

Answer 2

It would take 16.79 years, which could be rounded to 17 years for $8000 to grow to $14,400 at that rate. You can use the continuous compounding formula to derive this.