The PC financial is considering changing the method of compounding interest on line of credit accounts to daily compounding. If the current rate is 5.75% compounded quarterly, what nominal rate should PC Financial propose to maintain the same effective rate of interest?
A) 0.576%
B) 0.016%
C) 1.6%
D) 5.719%
E) 4.61%

Question

Quizplus · Accepted Answer

To maintain the same effective rate of interest, we need to find the nominal rate that when compounded daily gives the same result as 5.75% quarterly.

First, we need to convert the quarterly rate to an annual rate using the formula:

Annual rate = (1 + Quarterly rate)^4 - 1

Annual rate = (1 + 0.0575/4)^4 - 1
Annual rate = 0.059191

Now we can use the formula for daily compounding to find the nominal rate:

Effective annual rate = (1 + Nominal rate/365)^365 - 1

0.059191 = (1 + Nominal rate/365)^365 - 1

Solving for Nominal rate, we get:

Nominal rate = 5.719%

Therefore, the answer is D) 5.719%.

The PC Financial Is Considering Changing the Method of Compounding