Interest of 12% per year compounded monthly is roughly equivalent to an interest rate of 12.68% per year compunded yearly when using the formula: A=p(1+r/n)^nt

Question

If you solve the problem the two are equal; how can you derive 12.68% compounded yearly from 12% per year compounded monthly?

Answer 1

Let the rate compounded yearly be i

then (1+i)^1 = (1+.12/12)^12
1+i = 1.01^12
1+i = 1.126825
i = .1268..
so the annual rate is 12.68%

Answer 2

Thank you very much, that was most helpful.