### CFA Practice Question

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### CFA Practice Question

Which of the following statements is true?

I. If the compounding period is one year, stated annual interest is the same as effective annual interest.
II. If the compounding period is less than one year, effective annual interest is greater than stated annual interest.
III. If the compounding period is less than one year, stated annual interest is greater than effective annual interest.

User Comment
Rotigga This is wrong. Correct answer is I & III. For example, let m = 0.5, i = 0.08;
EAR = (1 + 0.08/0.5)^(0.5)-1 = 0.077 < Stated annual interest i
careywong I think II answer could be phrased better. I think if the compound period is less than 1 year, it means that the interest is actually paid more often...

So in your example, I think if m=0.5, it would mean that interest is paid twice a year and the EAR actually works out to 8.16%.

Correct me if I am wrong :)
MUTE Correct answer is I and II in the sence that, assume the compounding period of semiannually
EAR= (1+0.08/2)^2-1 this will give you 8.2% which is greater than Stated interest rate of 8%
sunj Note: Compunding period is one year. At the end of one year, the EAR would be same as stated, since the effect of compounding will be same.
broomhilda Rotigga,

m is the number of times per year that interest is compounded, you cannot set it equal to 0.5!
bobert It is a simple more periods = larger rate. I do not think that EAR can ever be smaller than the SAR, only equal or greater.

For example:
A given Periodic Rate = 4%. Say there was no compounding, but only just 4%, like the coupon on a bond payment which is not reinvested. For bonds the coupon is generally paid semiannually, so 2 periods. 2% + 2% = 4% which is the SAR. Seeing as how there is no compounding in this example, the EAR would also equal 4%. It is just that there is no compounding in this circumstance, so to call it EAR may not even be the best terminology. If it was compounded though, more periods will yield a higher return.

(1+.02)^2 - 1 = 4.04%

Hope that helps clear it up.
huyentrang Remember that "the compounding period is less than 1 year", means interest will be paid more than 1 time a year (m>1). So, EAR must be greater than SAR
SuperKnight I think the confusion here was compounding period (length of time) with the number of times within a year that that compounding occurs. The time in this case is less than one year which means that it will compound more than once a year. The 0.5 mentioned as an example of Rotigga's would not be less than 1 year as a time frame, it would actually be less than one time per year that compounding would occur and the time period would be longer than 1 year (so that example does not satisfy the question).
Raok yes EAR must either equal or greater than the stated rate
gill15 Super is right. Initially I thought it meant if payments happened if m<1 or once every m years which would make ii incorrect.

It means payments occur more then once a year. Tricky. Good.
msk500 Answers I and II are definitely correct. If compounding period is just 1 year, then the number of times compounding occurs in a year is 1. However, if compounding period is less than 1 year, for eg, every month or quarter, then the number of times compounding occurs in a year is more than one. As long as compounding occurs more than once in a year, the EAR is greater than the SAR.
ascruggs92 Rottiga, I see what you were thinking, but you can't have your M be less than one. For instance, if there is only one compounding period, M=1 and your annual and stated rate are the same. However, if you want to calculate how much interest you would earn over half a year, you wouldn't make M=0.5, M would now be two, your annual stated rate would be 8%, and your effective rate would be (1+0.08/2)^(2)= 1.0816. II is right
akbhagat96 Hi Everyone,
New to this forum. Can compounding period be grater then one year ??
nohuchi I. If the compounding period is one year, c/y = 1, stated annual interest is the same as effective annual interest.
II. If the compounding period is less than one year, c/y > 1, effective annual interest is greater than stated annual interest
III. If the compounding period is more than one year, c/y < 1, effective annual interest is less than stated annual interest