Please Help! Stuck on a word problem

Question

If the balance, M, at time t in years, of a bank account that compounds its interest payments monthly is given by M = M0(1.07763)t

(a) What is the effective annual rate for this account?

(b) What is the nominal rate?

Answer 1

Hi! I'm guessing that you meant to say that M = M0*(1.07763)^t, right? If that's so, a) The effective annual rate is 7.763% b) 1.07763 = (1 + r/12)^12 for monthly compounding, and r is the nominal rate. To solve for r: (1.07763)^1/12 = (1 + r/12) Rearranging, r = [(1.07763)^1/12 - 1]*12 = 0.075 = 7.5%