# Effective Interest Rate

• Jan 12th 2011, 07:39 AM
Mmike
Effective Interest Rate
I can't seem to get the right effective interest rate for the following question:

- Savings account with a nominal annual interest rate of 4.5%, compounded semi-annually, with interest payable monthly. Find the effective interest rate.

My process: (I'm not quite sure if I'm going the right way approaching this problem)
1. Finding the semi annually rate: EAR = [1+0.045/2]^2 - 1 = 1.04551-1 = 0.45516

2. Solving for monthly: [1 + 0.4551]^ (1/12) -1 = 0.0037 or 0.37%

I got 0.37% <---definitely wrong.

Any help/input will be greatly appreciated.
• Jan 12th 2011, 06:05 PM
Wilmer
"nominal annual interest rate of 4.5%, compounded semi-annually"
means effective of (1 + .045/2)^2 - 1 = 1.04550625 - 1 = .04550625 or ~4.55%

The frequency that the interest is paid does not affect this.
• Jan 13th 2011, 06:42 AM
Mmike
Quote:

Originally Posted by Wilmer
"nominal annual interest rate of 4.5%, compounded semi-annually"
means effective of (1 + .045/2)^2 - 1 = 1.04550625 - 1 = .04550625 or ~4.55%

The frequency that the interest is paid does not affect this.

If the question was nominal annual interest rate of 4.5%, compounded monthly, would the effective interest rate be 0.37% as calculated above?

Thanks.
• Jan 13th 2011, 11:15 AM
Wilmer
Quote:

Originally Posted by Mmike
If the question was nominal annual interest rate of 4.5%, compounded monthly, would the effective interest rate be 0.37% as calculated above?

Effective annual rate = (1 + .045/12)^12 - 1 = (1.00375)^12 - 1 = 1.045939825 - 1 = .045939825 or ~4.59%