# APR on a home mortgage **URL:** \ **Category:** Factual Questions\ **Created:** [January 28, 2022, 5:26pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580 "2022-01-28T17:26:55Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [January 28, 2022, 7:57pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/21 "2022-01-28T19:57:51Z")
> [@Saint\_Cad](#): > > In a pure math class yes. Teaching it via finances makes it different. The math of this kind of finance is simple. What is confusing to someone with math skills is just the unfamiliar terminology. Be clear on definitions, and don’t use the word “interest” ambiguously. ---
**Author:** ![RitterSport](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rittersport/32/6326_2.png) [@RitterSport](https://boards.straightdope.com/u/RitterSport)\ **Post date:** [January 28, 2022, 8:09pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/22 "2022-01-28T20:09:45Z")
> [@Saint\_Cad](#): > > Lesson 1: Show how interest changes when you increase the term of your car loan. (Goes up) > Lesson 2: Now calculate the APR for each term (Goes up) Is this right? If it were, I would expect APRs on 30 year mortgages to be substantially higher than 15 year mortgages, leaving aside the yield curve question. I thought that, with no fees, interest rate and APR are exactly the same, so the term wouldn’t affect it. ---
**Author:** ![md-2000](https://avatars.discourse-cdn.com/v4/letter/m/9d8465/32.png) [@md-2000](https://boards.straightdope.com/u/md-2000)\ **Post date:** [January 28, 2022, 8:56pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/23 "2022-01-28T20:56:49Z")
> [@RitterSport](#): > > Is this right? If it were, I would expect APRs on 30 year mortgages to be substantially higher than 15 year mortgages, leaving aside the yield curve question. I thought that, with no fees, interest rate and APR are exactly the same, so the term wouldn’t affect it. Finally. The very first post says “APR is (total interest and fees) ÷ (principal x time)”. This seems to be the first time someone has mentioned time. Without that, you can’t calculate APR. APR is basically “what proportion extra will this loan cost me over its lifetime, over and above the principle?” It makes it harder to hide exploding rates, fancy extra fees with other names, etc. A loan for $10,000 with $5,000 interest (plus fees) over 10 years, and a loan for $1,000,000 with $500,000 interest over 10 years, have the same APR. But - one loan I can afford, one I can’t. So essentially, APR is a valuable tool but not the only one necessary to judge a loan. A person who buys their house with a down payment of $10,000 or $50,000 will have the same APR but their monthly payments will be smaller with the larger down payment. Or, with the same monthly payment amount, pay off the smaller loan faster, and so less interest, smaller APR. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [January 28, 2022, 10:04pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/24 "2022-01-28T22:04:54Z")
> [@md-2000](#): > > Finally. Finally what? > [@md-2000](#): > > The very first post says “APR is (total interest and fees) ÷ (principal x time)”. This seems to be the first time someone has mentioned time. Without that, you can’t calculate APR. I’m not sure how OP could have mentioned time prior to his first post. And I have discussed several times the importance of distinguishing between a rate and an absolute or total amount. What do you think “rate” means? > [@md-2000](#): > > APR is basically “what proportion extra will this loan cost me over its lifetime, over and above the principle?” Because, ironically, you have omitted part of the concept of “rate” from this definition of APR. “Rate” does not mean the proportion extra over the lifetime, it means the proportion extra _per unit time_.🙂 ---
**Author:** ![Kent\_Clark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kent_clark/32/105_2.png) [@Kent\_Clark](https://boards.straightdope.com/u/Kent_Clark)\ **Post date:** [January 28, 2022, 10:33pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/25 "2022-01-28T22:33:58Z")
> [@Saint\_Cad](#): > > Lesson 1: Show how interest changes when you increase the term of your car loan. (Goes up) > Lesson 2: Now calculate the APR for each term (Goes up) > Student conclusion: higher APR means more real cost to the longer termed loan > Lesson 3: Show how your total interest when you increase the down payment on a house (Goes down) > Lesson 4: Now calculate the APR for each down (Stays the same) Lesson 4 should show how the total cost of the loan (and hence the house) goes down the more you pay up front/the less you borrow. If I put 50% down on the house and borrow less, the total cost I eventually pay will be less than if I put no money down and borrowed more. Not to mention that in my home town, the difference in interest rates between a 15- and 30-year fixed rate is almost a full percentage point, so Lessons 1 and 3 would end up showing students the same thing. ---
**Author:** ![Snipe70e](https://avatars.discourse-cdn.com/v4/letter/s/51bf81/32.png) [@Snipe70e](https://boards.straightdope.com/u/Snipe70e)\ **Post date:** [January 29, 2022, 6:22am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/26 "2022-01-29T06:22:55Z")
As most loan fees are a points. That is fees based on the size of the loan. Larger down payment would mean less fees therefore the ratio of fees to interest would be very close. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [January 29, 2022, 1:23pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/27 "2022-01-29T13:23:04Z")
> [@Saint\_Cad](#): > > No matter what your down payment is, the APR stays the same because it is a function of the loan amount NO ! . The loan amount is the amount loaned initially . Many many mortgages are for only 70%,50%,30% of the value of the property from the start. You can get a second mortgage, say you have 70% equity in a property, ie you owe 30% still, so you can get a second mortgage of up to 70%, rather than close the first mortgage, like in the olden days that wasn’t cheap if possible ??, and get a larger new mortgage. Every mortgage is only about the LOAN AMOUNT not the full value of the property. APR is about the initial balance , after the “down payment” … down payment is jargon anyway,it can mean deposit, so as to lock in the vendor to selling to you, or the minimum amount of equity to get the mortgage, or to get the mortgage at a cheaper interest rate , due to the lower risk to the lender, and avoiding mortgage insurance… ---
**Author:** ![Snipe70e](https://avatars.discourse-cdn.com/v4/letter/s/51bf81/32.png) [@Snipe70e](https://boards.straightdope.com/u/Snipe70e)\ **Post date:** [January 29, 2022, 5:01pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/28 "2022-01-29T17:01:51Z")
The APR is a function of the loan amount plus the fees charged. That is why you can get a loan at say 2.5% with an APR of 2.6% or maybe and APR of 2.8%. The APR verses the interest rate will give you an idea of the amount of fees charged. Most of the fees are based on the amount of the loan, but some fees are fixed. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [January 29, 2022, 9:44pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/29 "2022-01-29T21:44:26Z")
> [@Isilder](#): > > Many many mortgages are for only 70%,50%,30% of the value of the property from the start. You can get a second mortgage, say you have 70% equity in a property, ie you owe 30% still, so you can get a second mortgage of up to 70%, rather than close the first mortgage, like in the olden days that wasn’t cheap if possible ??, and get a larger new mortgage. What does any of this have to do with my scenario? Everyone else, once again, assume no fees. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [January 30, 2022, 12:11am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/30 "2022-01-30T00:11:49Z")
I think this is over complicated and is diluting what you are trying to teach. (What are you actually trying to teach?) The APR on a loan with no fees is just the basic interest rate. It is an input to the interest calculation and will only change if the interest rate is different between different loans. A short term car loan vs a long term car loan might the same interest rate or it might not. You can’t say a longer term loan will have a higher APR because it should actually be the same provided there are no fixed fees and the basic interest rate is the same. I think with lesson one and two you are leading your students astray by using loan figures that result in a different interest rate. That then causes confusion in lesson three and four when you discover that there is no need for the APR to change at all. Depending on the age of your students I’d be doing the following: Lesson 1. Given an interest rate of 7%. A long term loan vs a short term loan for the same amount. Which term results in the higher total interest paid? Answer. The longer term. Lesson 2. Given an interest rate of 7%. A bigger downpayment on a fixed price item results in a smaller loan. Do you pay more interest on a smaller loan or bigger loan over the same term? Answer, bigger loan equals more interest. (Seems blindingly obvious to me but I guess I learned this stuff somewhere.) Conclusion. Given a certain interest _rate_, borrowing more money and/or borrowing money for a longer time results in paying more in interest. To compare loans you need to compare both the interest rate and the term of the loan to work out which is more beneficial. It may be most beneficial to go for a long term loan with no penalty to make early payments. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [January 30, 2022, 5:29am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/31 "2022-01-30T05:29:30Z")
> [@Richard\_Pearse](#): > > Lesson 1. Given an interest rate of 7%. A long term loan vs a short term loan for the same amount. Which term results in the higher total interest paid? Answer. The longer term. > > Lesson 2. Given an interest rate of 7%. A bigger downpayment on a fixed price item results in a smaller loan. Do you pay more interest on a smaller loan or bigger loan over the same term? Answer, bigger loan equals more interest. (Seems blindingly obvious to me but I guess I learned this stuff somewhere.) > > Conclusion. Given a certain interest _rate_ , borrowing more money and/or borrowing money for a longer time results in paying more in interest. To compare loans you need to compare both the interest rate and the term of the loan to work out which is more beneficial. It may be most beneficial to go for a long term loan with no penalty to make early payments. As stated above, I’m already doing this. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [January 30, 2022, 5:54am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/32 "2022-01-30T05:54:21Z")
No, you are not doing this. The way you describe it you are deriving an APR from loan data. Then you wonder why in one case the APR changes but in another case it doesn’t. The reason for this is that one scenario uses different interest rates and the other one doesn’t. The students are getting confused because you have inconsistent variables. ---
**Author:** ![DesertDog](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/desertdog/32/11503_2.png) [@DesertDog](https://boards.straightdope.com/u/DesertDog)\ **Post date:** [January 30, 2022, 7:38am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/33 "2022-01-30T07:38:27Z")
It sounds like the puzzle with three men renting a hotel room for $30. They pay $10 each and go upstairs to the room. A few minutes after they leave, the clerk discovers the room rate should be $25 so he calls a bellhop over and gives him $5. “Give this to the guys in room 210.” In the elevator the bellhop thinks, _They won’t know what the rate is supposed to be,_ and pockets $2, giving the room-renters $1 each. So, now the men in the room have paid $9 apiece. 3x$9 = $27. This plus the $2 the bellhop kept = $29. Where did the extra dollar go? ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [January 30, 2022, 6:25pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/34 "2022-01-30T18:25:07Z")
> [@Richard\_Pearse](#): > > The way you describe it you are deriving an APR from loan data. Then you wonder why in one case the APR changes but in another case it doesn’t. The reason for this is that one scenario uses different interest rates and the other one doesn’t. The students are getting confused because you have inconsistent variables. Nope. Try again. For the car the nominal rate stays the same and the term changes thus the APR changes. For the house the nominal rate stays the same and the principal changes but the APR stays the same. I have already explained repeatedly part of the curriculum already is to look at how the total interest changes. The part I was missing was what Reimann filled in which basically is: what does it mean to be a different loan. That was already part of my instruction (in another lesson) and Reimann gave me idea on how to integrate that into this particular set of lessons. So thank you Riemann, you answered my question. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [January 30, 2022, 6:42pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/35 "2022-01-30T18:42:43Z")
Ok. Help me out here then. An APR on a loan with no fees IS the nominal rate isn’t it? In which case if the nominal rate hasn’t changed, neither has the APR. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [January 30, 2022, 7:11pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/36 "2022-01-30T19:11:20Z")
> [@Richard\_Pearse](#): > > An APR on a loan with no fees IS the nominal rate isn’t it? You are correct that the main difference is that (by law) the APR exposes hidden fees. But there may also be a slight difference attributable to the compounding period or the daycount basis for the interest rate calculation. If such a difference exists then unlike one-time fees it should be consistent across different terms. ---
**Author:** ![anny\_m](https://avatars.discourse-cdn.com/v4/letter/a/96bed5/32.png) [@anny\_m](https://boards.straightdope.com/u/anny_m)\ **Post date:** [January 30, 2022, 10:04pm UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/37 "2022-01-30T22:04:25Z")
Way too complicated for a normal high school class, but if you ever teach this to an AP class you can point out that, all other things being equal, paying $50,000 down on a $250,000 home will result in paying more dollars in interest than paying $25,000 down. But, unless you keep that extra cash in a jar buried in the backyard, there’s a cost to using that additional $25,000 for the down payment. Although you very likely (like almost 100%) can’t guarantee a rate of return on your investment that exceeds the interest rate on the mortgage, it is possible that if you put that $25k in an index fund and the market does well, you could end up better off financially at the end of the mortgage term by increasing the loan amount. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [January 31, 2022, 1:29am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/38 "2022-01-31T01:29:28Z")
> [@Richard\_Pearse](#): > > Ok. Help me out here then. An APR on a loan with no fees IS the nominal rate isn’t it? In which case if the nominal rate hasn’t changed, neither has the APR. Reimann answered this but I will point out that with the investment equivalent of rate of return (not CAGR) if you use simple interest then the RoR is the nominal rate. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [January 31, 2022, 4:07am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/39 "2022-01-31T04:07:25Z")
Reimann’s answer is not consistent with your contention that the APR changes when the term changes given a static nominal interest rate and no fees. Edit. In case it’s not clear, you are acting like Reimann is agreeing with you but I don’t think he is and I think you have a misconception about how changing the term of a loan affects the APR for a no fees loan. It doesn’t. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [January 31, 2022, 4:27am UTC](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580/40 "2022-01-31T04:27:46Z")
APR changes when the term changes on an amortized loan. That’s a fact. $50,000 loan 5% interest over 5 years =\> total interest = $6,613.70. APR = 6613.70 ÷ (50000 x 5) = 2.6455% $50,000 loan 5% interest over 6 years =\> total interest = $7,998.40. APR = 7998.40 ÷ (50000 x 6) = 2.6661% Show me your calculations that show the two APRs are the same Also, I never implied Reimann agreed with me. I’ve said like two or three times here that he corrected my misconception (or rather misrationalization) about home mortgages, down payments and APRs. [Previous page](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580.md?page=1) [Next page](https://boards.straightdope.com/t/apr-on-a-home-mortgage/958580.md?page=3)