how long will it take for $500 to triple in amount if interest is compounded continuously at 7.5%

Answer 1

When dealing with interest that is compounded continuously use the following formula:

Pe^(rt)

The "P" stands for principal and is the amount you start with, the e stands for Euler's number, there should be a button on your calculator with e that you use for this), the "r" stands for interest rate (always put your interest rate in decimal form), and "t" stands for time.

We know we are starting with $500 so that is our "P", our interest rate is .075, and we want our initial investment to triple (which would give us 500 * 3 = 1500). We don't know the time so that is what we are trying to find. Now plug everything into the equation:

1,500 = 500 * e^(.075t)

ln3 = ln*e^(.075t)

ln3/.075 = .075t/.075

t = 14.6