Exponential Functions · Exercise 69

The formula for the amount $A$ in an investment account with a nominal interest rate $r$ at any time $t$ is given by $A\left(t\right)=a{\left(e\right)}^{rt},$ where $a$ is the amount of principal initially deposited into an account that compounds continuously. Prove that the percentage of interest earned to principal at any time $t$ can be calculated with the formula $I\left(t\right)=e^{rt}-1.$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §6.1 Exponential Functions · Exercise 69