# Monthly Periodic Rate Example

At auction you buy an original artwork by an impressionist master as an alternative investment for \$9,875,000. You display and admire the painting for 2.5 years at which point you sell it for \$12,235,000. What is the monthly periodic interest rate, expressed as an effective annual rate (EAR), earned on the investment? a. 7.17% b. 8.6% c. 8.95% d. 7.04% Also, what is the annual compounded rate?

Monthly Rate = 0.7168% (FV = 12,235,000, PV = -9875000, n =30) EAY = (1+Monthly Rate)^12 - 1 = 8.9489% Annual Compound Rate = 8.9498% (FV = 12235000, PV = -9875000, n=2.5)

Not sure what you mean by “monthly periodic interest rate” but (12235/9875)^(1/30) - 1 = .007169. (1 +.007169)^12 = 8.95%=B.

you mean C

So, monthly periodic interest rate and annual compounded rate are the same?

No, monthly periodic is not the same as annual compounded: monthly is monthly, annual is annual (unless years are now called months). This is again a bad wording, that’s all, asking for the EAY on the basis of monthly rates.

Good for you map1. Just testing how to interpret the way they ask these questions.

What exactly does the quesiton mean? what is “the monthly periodic interest rate, expressed as an effective annual rate (EAR)” ?

EAY using monthly compounding.

As Dreary said, the monthly periodic interest rate, expressed as an effective annual rate (EAR) = EAY using monthly compounding. The reason its mentioned that way is to differentiate it from a “stated” annual rate with monthly effective compounding, which would just be Effective Monthly Rate X 12.

So in other words APR = 8.6%, APY (EAR) = 8.95%

The question is badly worded. EAY is EAY, which is annual compounding rate. It has nothing to do with monthly compounding. To see this, if it had not mentioned monthly compounding, simply ask “what’s the EAY for the investment”? I think the answer is still 8.95%. Correct me if I am wrong.

No, you could have EAY based on any sub period, so if you say EAY, you have to say how it is compounded. The same return could be stated as: 1) 8.95% annually compounded rate 2. 8.73% monthly compounded rate 3. 8.69% daily compounded rate 4.???% continuously compounded rate quiz: calculate 4.

8.57%

Dreary Wrote: ------------------------------------------------------- > No, you could have EAY based on any sub period, so > if you say EAY, you have to say how it is > compounded. > > The same return could be stated as: > > 1) 8.95% annually compounded rate > 2. 8.73% monthly compounded rate > 3. 8.69% daily compounded rate > 4.???% continuously compounded rate > > quiz: calculate 4. #4 is ln(1.0895) = 8.57%

Correct but why did you use 8.95% and not 8.73% or 8.69%? That’s fine, lets not complicate things too much.

I did ln(12235/9875) / 2.5 = .0857