PWC recently proposed to BMO to change the method of compounding interest on line of credit accounts to monthly compounding, as part of the marketing campaign. If the current rate is 2.5% compounded quarterly, what nominal rate should the PWC suggest to BMO executives to maintain the same effective rate of interest?
A) 0.208%
B) 2.495%
C) 3.773%
D) 2.5%
E) 2.75%

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) for quarterly compounding at 2.5% is calculated using the formula (1 + i/n)^(n*t) - 1, where i is the annual nominal interest rate, n is the number of compounding periods per year, and t is the time in years. For quarterly compounding at 2.5%, EAR = (1 + 0.025/4)^(4*1) - 1 = 2.516%. To maintain the same EAR with monthly compounding, we solve (1 + r/12)^(12*1) - 1 = 2.516% for r, which gives a nominal rate close to 2.495% when compounded monthly.

PWC Recently Proposed to BMO to Change the Method of Compounding