# Thread: Beginner Finance. Calculating EAR

1. ## 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

2. ## 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.)

3. ## Re: Beginner Finance. Calculating EAR

Originally Posted by ForeverConfused
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)

4. ## Re: Beginner Finance. Calculating EAR

Originally Posted by DenisB
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 $1,500 payment from a monthly annuity. You will receive the final payment from this annuity on July 1, 2018. The appropriate discount rate is 6%, compounded monthly. What was the present value of this annuity on December 31, 2015? In class we did the following for EMR:$\displaystyle EMR = (1+ .06/12)^1^2^/^1^2 -1$I understand why we do .06/12 since we are compounding monthly. I can't quite figure out why the exponent is equal to 12/12 5. ## Re: Beginner Finance. Calculating EAR I am guessing that EMR stands for equivalent monthly rate. Equivalent to what? The formula you have given makes no sense whatever.$\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.