Compound Rate as a Function of Market Interest Rate

Question

I have these two pictures from Investopedia. Here is the link to the page.

I am confused by this concept. How is the quarterly compound rate 11.825% with a 12% annual rate? Furthermore, how is the DAILY rate 11.66% when the annual rate is 12%.

This just doesn't make sense to me. Could someone explain this, and with that explanation tell me how I can get back from any of these rates (11.825%, 11.71%, 11.66%) back to 12%.

It seems that in the last two examples they are using 6 months (1/6) and 180 days (1/180) instead of 12 (1/12) months and 360(1/360) days in their exponent calculation. Is this an error or am I misunderstanding/misreading this information?

Answer 1

Generally this is referred to as the Annual Percentage Rate (APR), and the Annual Percentage Yield (APY). At the same percentage rate different compounding methods will generate different yields; with daily compounding being most preferable to the saver.

The basic concept is that interest accrues on the principle. Frequency at which the interest is counted toward your principle impacts your annual yield.

Daily

Day Principle   Interest
1   10000.00    3.33
2   10003.33    3.33
3   10006.67    3.34
4   10010.00    3.34
5   10013.34    3.34
6   10016.68    3.34
7   10020.02    3.34
8   10023.36    3.34
9   10026.70    3.34
10  10030.04    3.34
11  10033.38    3.34
13  10036.73    3.35
etc.

As you can see from here the interest is credited to you every day, as a result of this compounding effect your interest payments grow each every few days.

Monthly:

Mon.Day.Principle   Interest
1   1   10000.00    3.33
1   2   10000.00    3.33
1   3   10000.00    3.33
~~~~
1   27  10000.00    3.33
1   28  10000.00    3.33
1   29  10000.00    3.33
1   30  10000.00    3.33

2   1   10096.67    3.37
2   2   10096.67    3.37
2   3   10096.67    3.37
2   4   10096.67    3.37

As you can see here, the interest accrues on the principle every day, but its only credited at the end of the month. As a result your interest payments only increase at the beginning of the next month. This effect is again exacerbated in quarterly, semi-annual and annual compounding.