Continuous Compounding

Question

Suppose you can earn interest at some rate between 0% and 5%. Use your knowledge of the exponential function to explain why continuous compounding does not give you much of an investment advantage.

Answer 1

Suppose you invest $1 at 5% compounded yearly.

Suppose you invest $1 at 5% compounded continuously.

The 1st case gives you $1*(1.05)¹ = $1.05

The 2nd case gives you $1*e^0.05 = $1.051271

Compare the results.