Let's say you have a mortgage with a 5.00% APR. What that means is that the lender will divide 5% by 12 (or a very similar calculation) to get the equivalent monthly rate of interest they will charge on your mortgage. In other words, on a 5% APR loan, if you make no payments for a year* and if all fees and other penalties are waived, a balance of $1,000 will turn into a balance of $1,051.16.
| Month | Beginning | Ending | |
| 1 | $1,000.00 | $1,004.17 | |
| 2 | $1,004.17 | $1,008.35 | |
| 3 | $1,008.35 | $1,012.55 | |
| 4 | $1,012.55 | $1,016.77 | |
| 5 | $1,016.77 | $1,021.01 | |
| 6 | $1,021.01 | $1,025.26 | |
| 7 | $1,025.26 | $1,029.53 | |
| 8 | $1,029.53 | $1,033.82 | |
| 9 | $1,033.82 | $1,038.13 | |
| 10 | $1,038.13 | $1,042.46 | |
| 11 | $1,042.46 | $1,046.80 | |
| 12 | $1,046.80 | $1,051.16 | |
As you can see, a loan with a 5% APR, when compounded on a monthly basis, results in a balance that is 5.12% higher at the end of the year, so an equivalent annual simple interest for this loan would be 5.12%.
On the other hand, if you deposit $1,000 in your favorite financial institution at a 5.00% APY on January 1st, compounded daily, how much would you expect to get back on January 1st the next year? If you said anything more than $1,050, you would be wrong.
Whether compounded daily, monthly or quarterly, any APY rate is the exact equivalent simple interest percentage you would get on your deposited amount in one year.
* - this is only for the purpose of illustration - in real life, you definitely don't want to do this!!
