If APY factors compounding (while APR doesn't), shouldn't APY always be higher than APR?

Question

So, from what I understand:

• APR: rate advertised to borrowers (without compounding)
• APY: rate advertised to lenders (with compounding)

So, for a loan with APR of 6%, that compounds monthly:

• APY = (1 + (0.06/12)) ** 12 - 1 = 6.18%

However, let's now put these numbers in an Amortization Calculator:

Now if I'm a Lender, my APY would be total interest / loan amount, right?

Well, if I do:

• 3,279.72 / 100,000.00 = 3.28% (which is lower than 6.18%)

Why is this lower?

1. Does the APY for amortization schedules work differently (because interest is front-loaded or whatever)? But since the loan only lasts one year, how would that even make a difference?
2. How would things change if the loan lasted say, 5 years?

Answer 1

Why is this lower?

Does the APY for amortization schedules work differently (because interest is front-loaded or whatever)? But since the loan only lasts one year, how would that even make a difference? How would things change if the loan lasted say, 5 years?

It's lower because the monthly payment decreases the amount of principal that is subject to interest each subsequent month, and you aren't accounting for payments with your 6% APR calculation. You can see on the schedule that the interest for each month is 0.5% (6%/12) of the remaining principal from the prior month. You could say their net yield was 3.28% of the loaned amount, but since the loaned amount decreased each month it might not be the clearest way to illustrate the difference between APY and APR.

A simpler APR and APY illustration would be a scenario in which the amount subject to interest for the period is comparable (either no payments/additions or equivalent payments/additions) and the difference is due only to compounding.