In this last section of this chapter we have to look at some applications of exponential & logarithm functions.
Compound Interest
This first application is compounding interest & there are in fact two separate formulas which we'll be looking at here. Let's get first those out of the way.
If we were to put P dollars in an account which earns interest at a rate of r (written as a decimal) for t years (yes, it have to be years) then,
1. if interest is compounded m times per year we will have t m
A = P (1 + (r /m)^{tm}
dollars after t years.
2. if interest is compounded continuously then we will have
A = Pe^{rt }