Annual Percentage Yield on an account paying 6% interest

Question

Its compounded quarterly

Answer 1

Hi Sarah,

 

Step 1: Find the Periodic Rate (calculated by dividing the APR by the number of compounding periods in a year). In this case, the APR is 6% and the compounding periods per year is 4, which equates to quarterly.

 

Periodic Rate = 6/4 = 1.5% = .015  (the .015 is derived by taking 1.5%/100)

 

**If the interest were compounded monthly, you would divide by 12; if it is weekly, divide by 52**

 

Step 2: Add 1 to the periodic rate of .015 (note it should be in the decimal form NOT the fractional form)

 

1.015

 

Step 3: For a quarterly compounding, multiply 1.015 four times. You will get 1.0614.

 

1.015 * 1.015 * 1.015 * 1.015 = 1.0614

 

Step 4: Subtract 1 from 1.0614 and express it as a decimal .0614, converting it to a percentage by multiplying by 100 and you get an APY of 6.14%.

 

Remember: APY is larger than the APR if the compounding is less than a year. This will always be the case. The reason is because you're getting interest on the interest. Correspondingly, 1.015 compounded quarterly is expressed using power notation 1.015^4.

 

Hope this helps…All the best,
Dr. D.