loans and APR vs. APY

[Special K]

I have a question about exactly how interest is calculated for a loan, and how that relates to the terms APR and APY. I know how it works in the context of a savings account, as this information seems to be available on the HYSA's websites if you dig through the FAQs. For example, my HYSA compounds interest daily and is credited monthly.

As an example, if I deposit $10,000 into the HYSA described above with an APR of 5%, interest accrues daily - that is, the formula for the bank's recorded balance in my account is (where n = days):

balance[n] = balance[n - 1] + balance[n - 1]*0.05/365

Here, the APR is 5% and the APY is 5.13% due to the effects of compounded interest. I understand that part. What I am still a bit confused about is how this process works for loans. I can't seem to find a similar page on banks' websites that shows exactly how they calculate interest on their loans.

For example, let's say I borrow $10,000 at 5% interest. The repayment period will be 10 years, making the monthly payment $106.07. Would the bank call this 5% rate the APR? I originally thought interest was calculated on a monthly basis, and did not compound. That is, the interest for the first month would be:

$10,000 * 0.05/12 = $41.67

You therefore paid $64.40 in principal.

For the second month, the principal of the loan is now down to $9935.60, so the interest for the second month would be:

$9935.60 * 0.05/12 = $41.40, and so on.



However, I don't see how APY figures into this. The interest you owe is only calculated once per month so I don't see any compounding going on. Does APY even have any meaning with regard to loans, as opposed to savings accounts?

Are there loans who calculate the interest in other ways than what I have described above? For example, are there any loans who actually calculate the interest you owe daily and compound it - basically the savings account above in reverse?

Are all mortgages calculated using the method I described above, i.e. interest is calculated once per month, and does not compound?

 

[QED]

Most US mortgages are compounded on a monthly basis. Most HELOCS are compounded based on the average daily balance of the account, while most closed-end mortgages are compounded based on what your closing principal balance was (hence it usually does not matter whether you pay your mortgage three weeks early or a day early-- you will get charged the same interest).

For mortgages, much of the discrepancy between the APR and the interest rate at which the loan compouns are due to the upfront fees (such as closing costs and points) paid out when originating the loan. The APR is meant to give you an indication of the total cost of the loan over its term, so that you can do an "apples-to-apples" comparison to other loans with different rates, closing costs, and point requirements.