Every loan commercial I hear features something along the lines of the following:
“Right now we’re offering an excellent rate of 5.875% (6.05% APR) on fixed-rate mortgage loans, blah blah blah…”
Why are there two percentages given? I thought the only number involved was one APR. How are there two different percentage rates?
When they say 12%/year compounded monthly, they mean 1%/mo = 12.6825%APR
1% / month is not the same as 12% / year
1% / mo = 12.6825% /year
So someone like me who is not yet hip to this sort of thing is being slightly misled? I may be so cynical that this smacks of dishonesty to me.
I fully understand the math of compound interest, but what bothers me is that when I hear “12% APR” I’m inclined to think of simple interest, not compound.
I guess I’ll have to file this under the same deception category as “$99.99 is really the same as $100”.
Not really, sailor. Here is an explanation of why the “APR” (the second number) is higher than the “note rate” (the first number). Basically, the reason is that the APR folds in additional fees and points that you have to pay up front. It’s a way for the consumer to compare different mortgages. It’s obvious that a 6.0% mortgage with 1 point and $500 in fees is better than a 6.0% mortgage with 2 points and $1000 fees. But which is better, a 6.0% mortgage with 1 point and $500 in fees, or a 5.75% mortgage with 3 points and $750 in fees? Well, it depends. One way to compare is to amortize the up-front costs over the life of the loan, to get the “true” APR.
Here is an example of an APR calculator: type in your own points and fees to see how the APR changes.
I’d have to see the ad to be sure, but it’s possible in this example that both rates include points and fees. The difference, then, is that the 5.875% is a “force of interest”, or continuously compounded rate of interest. The 6.05% is the equivalent in annual simple interest. To convert between the two, take (e^0.05875)-1 = .0605.
Yes, the APR may include the effect of other things but my example is correct as a simple example.
You’re not being misled, you’re being protected. The annual percentage rate is a way of normalizing differently compounded interest rates, points, and fees to derive a single annual yield. The banks are required to report it – they’d rather not, because it always looks worse than the simple rate. The “simple interest” you’re looking for is relatively useless; it’s the APR that can be compared to other loan programs. If you persist in thinking that “annual percentage rate” somehow ought to mean “simple interest rate,” well, you’ve no one to blame but yourself.
Um, no. Loans like mortgages and credit cards accrue monthly.
I disagree. An example from this mortgage column:
This page, as well as all the other cites I was able to find, imply that the difference between the note rate and the APR is determined by additional fees, not by the difference between monthly and yearly compounding, as you claim. However, most of these pages also talk about the “very complex mathematical formula” used to determine the APR, so if you’ve got information to the contrary, I’m interested in hearing it. Is it possible you’re mixing up APR on a mortgage (which is what I believe the OP is asking about) and APR on things like credit card debt?
>> This page, as well as all the other cites I was able to find, imply that the difference between the note rate and the APR is determined by additional fees, not by the difference between monthly and yearly compounding, as you claim.
Look at your credit card statement and you will see that page is wrong. Look at any mortgage and you will see I am right. I am talking of my own experience. My example is correct.
The fact that interest accrues monthly does not dictate that a monthly rate be quoted in the ads. Assuming that the OP has posted actual numbers from an actual ad, it’s unlikely that they fit the continuous-to-annual conversion formula by coincidence.
>> The fact that interest accrues monthly does not dictate that a monthly rate be quoted in the ads
In every mortgage and credit card I have seen they mention a yearly rate which is compounded monthly and, therefore, the APR is higher. I do not know of any mortgages or credit cards which accrue continuosly. Can you show one? I am not saying they might not exist but I am saying they would be extremely uncommon.
I checked one of my credit cards and the interest compounds daily: .02836%(Daily) = 10.350% APR (I’ll assume their math is correct). As far as every mortgage I’ve seen, they compound monthly. I have never seen the constant “e” used in any commercial transaction.
No offense, but…what the heck are you talking about? I get the feeling that you and I are talking about different things.
What does a credit card statement have to do with the page I quoted? That page is about mortgages. The OP specifically asked about mortgages. I answered about mortgages. I gave a cite about mortgages. As far as I can tell, everything you’re saying applies to credit card debt and so forth, but not to mortgages.
I did take a look at my mortgage. My current mortgage has a note rate of 6.375%, with basically no up-front fees, and an APR of 6.385%. Doesn’t seem to me to be enough difference between the note rate and the APR to be the result of a simple/compunded interest difference. Another example: Here’s a credit union that offers zero point/zero fee mortgages. Note that the APR is the same as the note rate.
I believe your example to be incorrect. The difference between the note rate and the APR for mortgages is not the difference between monthly and yearly compounding. I have provided numerous examples to support my belief. Please either clarify your statement (if I have misrepresented it) or provide some relevant cites to back it up.
All right, I see that I was misled by the term “Annual Percentage Rate”. Quoting from “The Theory of Interest” by Stephen G. Kellison:
So, despite it’s name, the APR isn’t really annual. The compounding doesn’t come into play–either as continuous-to-annual (as I was trying to do; I was misled by the coincidence within the rates cited by the OP) or as monthly-to-annual as sailor was trying to do.
It appears that the only difference between the note rate and the APR is points, fees, and closing costs, as argued by zut.
Good info. By the way, I was not quoting actual rates from a commercial in the OP. It was just an example.
>> So, despite it’s name, the APR isn’t really annual.
The Annual Percentage Rate is not annual? Hmmmm… Ok. Whatever.
I am quite sure the APR is the true cost of borrowing the money for any loan, whether credit card or mortgage. APR is not defined differently depending on the type of loan. And it is the annual cost of borrowing including everything (and “everything” includes compounding as my credit card example shows).
My only experience with Truth In Lending has been in mortgage lending. It’s been nearly 10 years, but prior to that, I dealt with this issue almost daily for more than 20.
The original T-I-L was passed in about 1969, and it was only at the last minute that Congress added mortgage lending. So the terms, methods etc have always been difficult to fully understand. The law and regulations have been changed many times but not the basic idea.
In regard to mortgage lending, here’s the basic idea.
Certain fees, like points, are finance charges. All finance charges(except interest not collected at closing) are subtracted from the initial note amount. That equals the “amount financed”.
You will see right off that “amount financed” might lead some people to believe it means the amount borrowed, but for TIL purposes that’s not (necessarily) true.
OK, the basic calculation is like this. Determine the interest rate(APR), so that the future payments(which were calculated on the note amount) and the amount financed mesh. What APR will require those payments?
Variable rate mortgage loans came along well after the original law. It quickly because practice to offer an initial rate lower than the “index plus margin” shown in the loan documents. The additional complexity in variable rate mortgages relative APR, is that one must calculate the anticipated future payments based upon the assumption the “index” will never change!
The APR is not used in any way to charge or collect interest from the customer. It’s only for advertising and disclosure purposes. At one time the APR was required to be shown if monthly billings(for mortgage loans) were used but was later repealed for mortgage loans. I don’t know the status now.
I am sorry if my previous post sounded a bit snippy as I did not intend it.
To expound and compound on what I have posted: The definition of APR is “the annual loan rate which makes the present value of all loan payments equal to the net proceeds to the borrower on the loan date”. In other words, it includes everything. A loan (mortgage or otherwise, no points or fees) quoted as 12% and compounded monthly (as almost all mortgages are compounded) really means 1% per month. Now apply the definition above and you get an APR of 12.6825%.
In http://www.assurelink.ie/regulationresource/mort/sch4.htm you can see the formula states “tK is the interval, expressed in years and fractions of a year”.
I cannot see how you could leave the compounding effect out as, in fact, you calculate the APR from the actual payments. In my credit card example the daily rate is .02836% and the yearly rate (not compounded) would be 365 times that which is under 3% but that is not the APR which is higher because it takes into account the compounding (as well as any fees or expenses if they existed).
And, I do not believe APR is defined differently for different kinds of loans. I’d like to see some proof to the contrary. APR is a wide concept for loans and investments. When you invest money your bank quotes you an APR too.
(1)The APR is a valid overall comparison between two loans of equal duration if they are both carried to the end (not prepaid). If there is a chance of prepayment a loan with a higher APR may turn out to be the better deal.
(2) There is no direct formula which allows for the calculation of APR and it has to be done by successive approximations. This is very easily done with a spreadsheet. Give me any set of conditions (Loan amount, points, fees, payments) and I can tell you the APR. I can also compare two loans for prepayment options. I have been doing this for quite a while now. I have asked the question of loan copmparisons in other threads but there were no takers. If anyone is interested we can go into it here.