I was reviewing continous interest formulas when something stumped me. The accepted formula for continous interest is A=Pert, and the proof of it is simple enough to understand. However, my math book solves the formula in a different way. It starts with the standard model for growth rate, P=P0ekt, and than solves for k. Example: Determine how much money will exist in an account if Ed deposits 1000$ in an account with 5% interest for 5 years. Case 1: A=Pert A=1000e(.05)(5) Case 2: P=P0ekt P=1000ekt Evaluate the amount at one year to solve for k. 1000(1.05)=1050 1050=1000ek(1) Solve for k. 1050/1000=ek(1) k=ln(1.05) P=1000eln(1.05)t The growth constants are different in both cases. What is the cause of this?