Annual Return and Compounding

Course: Fundamentals of Financial Planning
Lesson 5: Using the Calculator

Student Question:

My question relates to being able to clearly distinguish when the CFP Board exam will require an annual, or other period for the answer.
Question 5(b) asks: “What is the rate of return on Investment 2 using daily compounding?”

What is the annual rate of return on Investment 2, made 3 years ago for $50,000 and worth $191,000 today, using daily compounding? Round your answer to two decimal places.

  • 35.32%
  • 39.32%
  • 41.31%
  • 44.70%

The answer requires to multiply by 360 to make it annual, but the question states: “using daily compounding”.

On the CFP Board exam, my guess is they could have included the daily compounded answer of .1242, and also the correct answer – the annual number of 44.70 as alternatives. 

So my questions is, what is the smartest way to look at this, and do you think there may have been a typo in the question where it actually does ask for the “daily” answer (unless I’m missing something).

Instructor Response:

Great question here.  As you can see, it’s very important to wade through the details of each question, especially when dealing with calculation questions. 

First, let’s define these two terms.

  1. Return/annual return
    1. keep in mind that return is different than compounding. Return is easy, it’s the return on my investment. It’s the money I made or lost.
    2. Annual return (or monthly return or any other period) is what rate of return I make during that period.
  2. Compound(ing)
    1. Compounding is the process in which an asset’s earnings are reinvested.  Daily compounding means the return every day is reinvested.  Monthly compounding would mean it’s reinvested only on a monthly basis.

So now to question 5 from this page.  The question starts by saying, “You are calculating the average annual return….”  So for all of these choices, you are asked for an annual return.   From there, we are given different scenarios on how often to compound.

On the board exam, unless told differently, you would assume annual return and compounding.  But this question tells you specifically to use daily compounding.  So keep in mind that return and compounding are two different terms, and you need to be clear on what the question is asking for on each.

Does that help clarify here?  Let me know