An initial investment of 3000 doubles in value in 8.3 years. assuming continuous compounding, what was the interest rate?

To solve this we are going to use the continuous compounding interest formula:

where:
is the amount after  years.
is the initial investment.
is the Euler's constant.
is the interest rate.

Since we know from our problem that the investment of 3000 doubles in value in 8.3 years, . We also know that  and , so lets replace those values in our equation:


Notice that thing we are trying to find, , is in the exponent; therefore, we must use logarithms to bring it down:







The only thing left now is multiplying our rate by 100% to express it as a percentage:
%

We can conclude that the continuous compounding interest rate needed to double $3000 in 8.3 years is approximately 8.4%.