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Thread: Beginner Finance. Calculating EAR

  1. #1
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    Beginner Finance. Calculating EAR

    I'm having trouble figuring out when to calculate EAR or the effective monthly rate, effective daily rate etc. How do I know when to calculate which one? Also I don't quite understand the formula. How do I know how many compounding periods I need to divide the interest rate by and then raise it to the same exponent in the equation

    EAR = (1 + i/n)^n - 1
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  2. #2
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    Re: Beginner Finance. Calculating EAR

    "i" is a percentage rate per what time interval? If, as is usual, r is the percentage rate per year, and the interest is compounded annually, then n is the number of years in the interval. If the interest is compounded monthly, then n is the number of months in the interval (one year, 12 mo, two years, 24 mo, etc.) If the interest is compounded daily, then n is number of days in the interval (one year 365 days, two years 730 days, etc.)
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  3. #3
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    Re: Beginner Finance. Calculating EAR

    Quote Originally Posted by ForeverConfused View Post
    I'm having trouble figuring out when to calculate EAR or the effective monthly rate, effective daily rate etc. How do I know when to calculate which one? Also I don't quite understand the formula. How do I know how many compounding periods I need to divide the interest rate by and then raise it to the same exponent in the equation

    EAR = (1 + i/n)^n - 1
    Hard to tell what you're really asking;
    can you supply an example?

    Let's take "effective monthly rate";
    assume 1000 dollars accumulating
    to 1200 over 1 year: eff. mo. rate = ?

    1000(1 + i)^12 = 1200

    (1 + i)^12 = 1200/1000 = 6/5

    1 + i = (6/5)^(1/12) ******

    i = (6/5)^(1/12) - 1

    i = .0153....

    So rate 1.53% compounded monthly.

    ******rule: if a^p = b then a = b^(1/p)
    Last edited by DenisB; Jan 25th 2017 at 11:19 AM.
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  4. #4
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    Re: Beginner Finance. Calculating EAR

    Quote Originally Posted by DenisB View Post
    Hard to tell what you're really asking;
    can you supply an example?

    Let's take "effective monthly rate";
    assume 1000 dollars accumulating
    to 1200 over 1 year: eff. mo. rate = ?

    1000(1 + i)^12 = 1200

    (1 + i)^12 = 1200/1000 = 6/5

    1 + i = (6/5)^(1/12) ******

    i = (6/5)^(1/12) - 1

    i = .0153....

    So rate 1.53% compounded monthly.

    ******rule: if a^p = b then a = b^(1/p)
    Here is an example of a question we did in class

    On January 1, 2016 you received a $1,500 payment from a monthly annuity. You will receive the final payment from this annuity on July 1, 2018. The appropriate discount rate is 6%, compounded monthly. What was the present value of this annuity on December 31, 2015?

    In class we did the following for EMR:

    EMR = (1+ .06/12)^1^2^/^1^2 -1

    I understand why we do .06/12 since we are compounding monthly. I can't quite figure out why the exponent is equal to 12/12
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  5. #5
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    Re: Beginner Finance. Calculating EAR

    I am guessing that EMR stands for equivalent monthly rate. Equivalent to what?

    The formula you have given makes no sense whatever.

    $\left ( 1 + \dfrac{0.06}{12} \right )^{12/12} - 1= (1 + 0.005)^1 - 1 = 1 + 0.005 - 1 = 0.005 = \dfrac{0.06}{12}.$

    In other words, you have given a complex expression for a simple fraction.

    $ \left ( 1 + \dfrac{0.06}{12} \right )^{12} - 1$

    is the annual simple interest rate equivalent to an annual rate of 6% compounded monthly. I have no idea why that is called EMR. I think you need to clean up your notes and get concepts straight before you worry about formulas.
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