I managed to prove the equation for compound interest when interest is compounded continuously.
FV = P*e^rt Where FV = future value, r = interest rate and t = years invested.
I was now wondering how i would begin to expand the above equation so that it can take into account any regular deposits put it into the investment. Lets say for convenience I am going to add £k every year. Note that k is a constant so it wont change. How would i form an equation for these regular deposits?