Question on Effective and Equivalent Interest Rates (Compound Interest)

  • Hello business math professors,
    I’m in the process of creating the 4th edition of our “Mathematics of Business and Finance” textbook and I wanted to know your thoughts on combining the following two sections of Ch. 9 in our book:
    Section 9.7 - Calculating Effective Interest Rate and
    Section 9.8 - Calculating Equivalent Interest Rate.
    As you are aware, effective interest rate (annual compounding interest rate) is a subset of equivalent interest rate. This is why I am thinking of combining these two sections into one.
    For your reference, you can download the sections directly from here:
    (Section 9.7) Calculating Effective Interest Rate
    (Section 9.8) Calculating Equivalent Interest Rates
    I look forward to hearing from you.

  • The sections can be combined in a single section “equivalent compound interest rates”.
    My suggestion is to emphasize once more that the annual effective rate is useful when we compare investments that have interest rates with different compounding periods and to have a solve example with 3-4 investments with interest rates compounded semi-annually, quarterly, monthly and /or daily, (for example 3.19 % cs, 3.18c.q, 3.17c.m.) and to identify the best investment ( to rank the rates from the lowest to the highest based on their equivalent effective rate)
    Investment A ( interest rate 3.19% c.s has the effective rate 3.215%)
    Investment B ( interest rate 3.18% c.q. has the effective rate 3.218%)
    Investment C ( interest rate 3.17% c.m. has the effective rate 3.216%)
    B, C, A with B the best investment.
    Have one question or solved example when the effective rate is given and they have to determine the equivalent/corresponding nominal rate ( sc.s, cq, cm).

  • @Kuga Thanks for bringing this up, Kuga.
    I support the idea of merging the two sections since an Effective Interest Rate is just a modification of an Equivalent Interest Rate. The new section can be named after Equivalent Interest Rates with "f" as a special case.

  • I'm all in favour of reducing the number of interest rate formulas we need to remember, so combining the two sections could accomplish that by saying that the effective annual rate formula is identical to the equivalent periodic rate formula when the target compounding frequency in the former is m2 = 1.

    It seems to me there is really just one formula that has two uses.

    When we have a set of nominal rates of differing compounding frequencies, and we want to rank the set of rates, then we set m2 =1 to obtain the effective annual rate.

    When we want to convert one nominal rate into another having a different compounding frequency, then we use the more general equivalent periodic rate version of the formula while setting m2 to the value of the target compounding frequency.


  • I think merging the two- equivalent and effective interest rates- into one section, is a terrific idea!
    As both Paul and Alex pointed out, this can be used to highlight that they are related, and how. I also like Mariana's idea, that a good example comparing the effective rates, of 3-4 investments with different compounding frequencies, to compare the effects and identify the best investment, would be a very worthwhile addition. This is certainly something I present, and having such an example in the text for the students to refer to, is another great suggestion!


  • I think it's a good idea to combine the two sections. It should help student to understand that effective interest rates are just a special case of equivalent interest rates.


  • I also like the idea of merging the two sections.


  • I like the two sections merged. They make sense together as effective rate is just a specific case of equivalent rate.