What is the effective annual interest rate when you have money nominally compounding at 10%pa?
e0.10= 0.1052 = 10.52% Putting this into a present value formula: FV = PV eit Where FV = future value (or account balance a time t) PV = present value (or account balance at the start) i = nominal interest rate and t = time in years to invest. This next bit is optional for someone that doesn’t want to know about calculus, but I have explained things in small enough steps that any high school graduate that did a bit of calculus should be able to follow the thread. Using calculus it can be proven that this is the correct way to express continuously compounding interest, where FV = the balance at time t and PV is the present account balance. d/dt means “taking the derivative with respect to variable t”, which means the same thing in this case as “to find the rate at which FV changes over time”. Now in basic calculus we know that e has some unusual properties, when you find the derivative with respect to x of e raised to something the derivative always equals the exponent’s derivative with
