I've bragged in the past about my market timing acumen, which tends to favour the party sitting opposite me in any transaction. I tend to dwell on my past decisions, but only to the point of nodding sadly in lament of my knack for choosing the wrong time to pull the trigger. These decisions don't consume me, but I can easily count them off for you on a moment's notice.
Not this time, however.
The Loonie household mortgage was up for renewal last month, so Ms. Loonie and I checked out the rates available to us. We were able to renew with our current lender for a 3-year fixed rate of 2.65%, more than 2% lower than our previous rate. The day after we signed the papers, rates jumped by 50 basis points, so we literally slid in just under the wire, and guaranteed ourselves three years of low-rate home ownership. I'm sure a strong negotiator with excellent credit could still have secured a lower rate, but given the ease of the transaction, I'm pretty confident in saying that we locked in "at the bottom".
But that's not all. Since I was at the branch anyway, I decided I would talk to the bank about managing our own property tax payments. Since our mortgage is high-ratio (more than 80% loan-to-value), the bank has been collecting property tax payments from us, and paying the city on our behalf. Now that we've mastered the art of partitioning our savings, we decided that we'd rather pay the city directly, and have more control over the balance in this account (and hey, why not earn some interest on it while we're at it?). This change turned out to be very straightforward as well. The tax portion of our bi-weekly mortgage payment has been eliminated, and I've set up a bi-weekly transfer of the appropriate amount to a dedicated savings account.
We're now making much faster progress on the mortgage, and we're in control of our property tax payments. Easy as pie, right?
Until I realize that, as a side-effect of the CUPE strike currently underway in the GTA, there's nobody manning the phones in the city revenue office to take our lender off the tax account.
Great timing.
Showing posts with label Mortgage. Show all posts
Showing posts with label Mortgage. Show all posts
Thursday, July 2, 2009
Thursday, March 5, 2009
Payday update - under $300K edition
I haven't done one of these in a while, but with today being payday, I thought I'd provide a quick update of my financials. My NCN Network chart has been updated with my latest revolving debt numbers.
Revolving debt is down to $14,212.71, which means I've paid off over 48% of the $27,610.74 I had when I started keeping track in April of 2007. Another $407.34, and I will have paid off half of my revolving debt. That's highly motivating.
Student loans are also dropping nicely. I recently renegotiated Ms. Loonie's interest rate, so both our loans are now at a fixed rate of 5%. Two more payments will bring my loan under $4,000, and hers under $17,000. Compare that to the respective $7,687.35 and $26,000 that we started with, and you can see the progress we've made over the past two years.
Finally, the really exciting news is that today's mortgage payment brought our principal down below $300,000, and we currently owe $299,883.42 on our mortgage. Granted, two weeks' accrued interest will boost the amount owing back up above $300K, but this is a huge milestone for us. It seems like only yesterday we finally bid adieu to our CMHC premium, but now we have a new first digit, and with our renewal date approaching and rates at all-time lows, we are in better shape every day.
I think it's safe to say that I'm happy with our progress.
Revolving debt is down to $14,212.71, which means I've paid off over 48% of the $27,610.74 I had when I started keeping track in April of 2007. Another $407.34, and I will have paid off half of my revolving debt. That's highly motivating.
Student loans are also dropping nicely. I recently renegotiated Ms. Loonie's interest rate, so both our loans are now at a fixed rate of 5%. Two more payments will bring my loan under $4,000, and hers under $17,000. Compare that to the respective $7,687.35 and $26,000 that we started with, and you can see the progress we've made over the past two years.
Finally, the really exciting news is that today's mortgage payment brought our principal down below $300,000, and we currently owe $299,883.42 on our mortgage. Granted, two weeks' accrued interest will boost the amount owing back up above $300K, but this is a huge milestone for us. It seems like only yesterday we finally bid adieu to our CMHC premium, but now we have a new first digit, and with our renewal date approaching and rates at all-time lows, we are in better shape every day.
I think it's safe to say that I'm happy with our progress.
Thursday, July 10, 2008
Changes coming to Canadian mortgages
The Finance Department announced yesterday that it would shorten the maximum amortization on government-backed mortgages from 40 to 35 years, in an effort to prevent a housing bubble in Canada. The maximum was raised in 2006 from 25 to 40 years, in response to the boom in demand for Canadian real estate. In addition to shorter amortizations, the minimum down payment required will be raised from 0% to 5%.
These changes come into effect on October 15, which means we can likely expect an uptick in home purchases over the next few months, as buyers look to sneak in under the wire with the old lending rules. After that, things may cool off a bit with the tighter rules.
I think this is a good idea in principle, but I wonder a bit if it's too little, too late. We've essentially had two years of relaxed lending rules to rack up a lot of long-term, high-ratio mortgages, and drive up housing prices. Will this change really work to make buyers think twice about the costs of homeownership? Also, although the new rules will be tighter, they still allow a 35-year, 95% mortgage, which is still a pretty highly leveraged position.
In Canada, the saving grace of our real-estate situation is the near absence of sub-prime lending (the Finance Department pegs this at about 5%). Most of the people who take out a mortgage to buy a home in Canada actually meet prescribed lending criteria, and they know the terms of their mortgage (as opposed to ARMs and negative-amortization loans). So we're likely not looking at the same default and foreclosure situation that we've seen in the U.S. over the past year.
The future of real estate prices in Canada, however, is far from certain. It should be an interesting ride.
These changes come into effect on October 15, which means we can likely expect an uptick in home purchases over the next few months, as buyers look to sneak in under the wire with the old lending rules. After that, things may cool off a bit with the tighter rules.
I think this is a good idea in principle, but I wonder a bit if it's too little, too late. We've essentially had two years of relaxed lending rules to rack up a lot of long-term, high-ratio mortgages, and drive up housing prices. Will this change really work to make buyers think twice about the costs of homeownership? Also, although the new rules will be tighter, they still allow a 35-year, 95% mortgage, which is still a pretty highly leveraged position.
In Canada, the saving grace of our real-estate situation is the near absence of sub-prime lending (the Finance Department pegs this at about 5%). Most of the people who take out a mortgage to buy a home in Canada actually meet prescribed lending criteria, and they know the terms of their mortgage (as opposed to ARMs and negative-amortization loans). So we're likely not looking at the same default and foreclosure situation that we've seen in the U.S. over the past year.
The future of real estate prices in Canada, however, is far from certain. It should be an interesting ride.
Thursday, July 3, 2008
Feeling some property tax relief
Both Paid Twice and Make Your Nut posted recently about changes to their property tax payments. Like many new homeowners, they make escrow payments to their mortgage lender in order to cover their periodic property tax expenses, and like many new homeowners, they started off with an escrow shortage, and subsequently saw their payments jump to cover the shortfall.
Ms. Loonie and I have been in a very similar situation. We make a property tax payment to our bank every two weeks along with our mortgage payment, and this is meant to cover our property tax bill when it arrives. Because we had a tax bill to pay shortly after closing on our condo, we initially found ourselves behind on our tax payments, and the bank hiked our bi-weekly contribution as a result. Now that we've got two years of payments under our belt, however, we're finally getting caught up on our initial shortfall, and I've been thinking of talking to the bank to get the payments adjusted back down.
Well, it turns out the adjustment letter we received last summer was just part of an automatic review the bank does on the account every year, as we received an almost identical letter from them this year. The only difference is, this time around the payments are being reduced rather than increased.
It's nice to see that the bank is actually proactive with managing the property tax account. I'd still prefer to pay the taxes ourselves (and I think we'll look into this when we renegotiate next summer), but it was a nice surprise to see the lender adjust our payments down without having to ask.
Like Paid Twice and Make Your Nut, we'll have a bit of extra cash injected into the budget once the payments readjust (effective August 21). It amounts to about $100 per month for us, which is certainly welcome. This was a nice instance of seeing something I read on a couple of American blogs relate directly to my own situation here in Canada. Another illustration that, although the terminology may differ, our financial systems operate in very similar ways on either side of the border.
Ms. Loonie and I have been in a very similar situation. We make a property tax payment to our bank every two weeks along with our mortgage payment, and this is meant to cover our property tax bill when it arrives. Because we had a tax bill to pay shortly after closing on our condo, we initially found ourselves behind on our tax payments, and the bank hiked our bi-weekly contribution as a result. Now that we've got two years of payments under our belt, however, we're finally getting caught up on our initial shortfall, and I've been thinking of talking to the bank to get the payments adjusted back down.
Well, it turns out the adjustment letter we received last summer was just part of an automatic review the bank does on the account every year, as we received an almost identical letter from them this year. The only difference is, this time around the payments are being reduced rather than increased.
It's nice to see that the bank is actually proactive with managing the property tax account. I'd still prefer to pay the taxes ourselves (and I think we'll look into this when we renegotiate next summer), but it was a nice surprise to see the lender adjust our payments down without having to ask.
Like Paid Twice and Make Your Nut, we'll have a bit of extra cash injected into the budget once the payments readjust (effective August 21). It amounts to about $100 per month for us, which is certainly welcome. This was a nice instance of seeing something I read on a couple of American blogs relate directly to my own situation here in Canada. Another illustration that, although the terminology may differ, our financial systems operate in very similar ways on either side of the border.
Monday, April 7, 2008
Mortgage options: is Cash Back a good deal?
With this weekend's balmy double-digit temperatures, we Canadians have finally been given a taste of spring. The sun is rising earlier and setting later, temperatures are rising, and our SAD is finally lifting.
And, of course, the mortgage advertising is once again beginning in earnest. With the majority of home sales closing between April and August, spring is the prime season for banks to push their mortgage lineup. Now that we've survived RRSP season, and are wrapping up our tax returns, it's time to be bombarded with mortgage rates and special promotions.
One of the products I've seen advertised this year is a "cash back" mortgage. Basically, when your bank advances the mortgage, you receive a percentage of the principal as a cash reward. You can then use this money for whatever you want. The banks want you to use this to pay for furniture, renovations, or vacations, but you can also use the full cash amount as a lump sum mortgage payment.
The typical trade-off with cash back mortgages is that you have a longer term and higher rate than a standard mortgage, so although you get some immediate cash in hand, you end up paying more in interest in the long run. I thought I'd have a look at the numbers, to determine just how good or bad this offering really is.
Assuming that the borrower is making bi-weekly rapid payments (i.e. paying half the monthly amount every two weeks), the principal remaining at the end of the term will be $256,132 for the standard mortgage holder (5.70% rate), and $258,710 for the cash back borrower (7.20% rate). When you factor in the $15,000 cash reward, the cash back borrower ends up $12,422 ahead of the standard mortgage holder. If the $15,000 amount earns 3% interest in a savings account during the 5-year term, this increases to a $14,842 spread. If, on the other hand, the full $15,000 is used to make an immediate lump sum payment on the mortgage, the spread is even higher, at $18,600.
On the face of it, cash back seems to be an attractive option.
However, we're only looking at one side of the picture. The higher interest rate paid by the cash back borrower translates to a higher bi-weekly payment. In this example, the cash back borrower has made a total of $138,999 in mortgage payments, whereas the standard mortgage holder has paid only $121,307. That means the cash back borrower had to pay $17,692 more than the standard mortgage holder, which puts them behind by $2,850 unless the $15,000 was used as an immediate lump sum payment, in which case cash back comes out ahead by a mere $909. Even that $909 spread is barely a 2% return on the extra $136.09 in payments made every two weeks throughout the term.
If you can afford the extra payments that would come with the cash back mortgage, then you can always increase the bi-weekly payment amount on your standard mortgage, and make even faster progress in paying off the principal.
And, of course, the mortgage advertising is once again beginning in earnest. With the majority of home sales closing between April and August, spring is the prime season for banks to push their mortgage lineup. Now that we've survived RRSP season, and are wrapping up our tax returns, it's time to be bombarded with mortgage rates and special promotions.
One of the products I've seen advertised this year is a "cash back" mortgage. Basically, when your bank advances the mortgage, you receive a percentage of the principal as a cash reward. You can then use this money for whatever you want. The banks want you to use this to pay for furniture, renovations, or vacations, but you can also use the full cash amount as a lump sum mortgage payment.
The typical trade-off with cash back mortgages is that you have a longer term and higher rate than a standard mortgage, so although you get some immediate cash in hand, you end up paying more in interest in the long run. I thought I'd have a look at the numbers, to determine just how good or bad this offering really is.
Example
To illustrate the trade-off between a cash back and standard mortgage, I'll look at the costs of the cash back mortgage, and compare them to the costs for a standard mortgage with a lower rate. For my calculations, I made the following assumptions:- $300,000 mortgage, with 25-year amortization
- 5-year term, with 7.20% posted rate
- 5% cash back vs. 1.50% discount on mortgage rate
Assuming that the borrower is making bi-weekly rapid payments (i.e. paying half the monthly amount every two weeks), the principal remaining at the end of the term will be $256,132 for the standard mortgage holder (5.70% rate), and $258,710 for the cash back borrower (7.20% rate). When you factor in the $15,000 cash reward, the cash back borrower ends up $12,422 ahead of the standard mortgage holder. If the $15,000 amount earns 3% interest in a savings account during the 5-year term, this increases to a $14,842 spread. If, on the other hand, the full $15,000 is used to make an immediate lump sum payment on the mortgage, the spread is even higher, at $18,600.
On the face of it, cash back seems to be an attractive option.
However, we're only looking at one side of the picture. The higher interest rate paid by the cash back borrower translates to a higher bi-weekly payment. In this example, the cash back borrower has made a total of $138,999 in mortgage payments, whereas the standard mortgage holder has paid only $121,307. That means the cash back borrower had to pay $17,692 more than the standard mortgage holder, which puts them behind by $2,850 unless the $15,000 was used as an immediate lump sum payment, in which case cash back comes out ahead by a mere $909. Even that $909 spread is barely a 2% return on the extra $136.09 in payments made every two weeks throughout the term.
Conclusion
Clearly, when you take into account the larger minimum payments that come with a cash back mortgage, it becomes a lot less appealing. The only way to come out ahead versus a standard, lower rate mortgage, is to throw in the whole cash reward as a lump sum payment at the beginning of the term. Even if you do this, however, you're not likely to keep up with inflation, so it's a far better idea to take a standard mortgage with a lower rate.If you can afford the extra payments that would come with the cash back mortgage, then you can always increase the bi-weekly payment amount on your standard mortgage, and make even faster progress in paying off the principal.
Tuesday, January 29, 2008
Question for the readers: CMHC at mortgage renewal?
I have a question for those Canadian homeowners and mortgage experts out there.
As I've mentioned in the past, Ms. Loonie and I bought our condo using a CMHC-insured, high-ratio mortgage. We've since paid off our CMHC premium, and are now making progress on the "real" mortgage principal. Our mortgage will be up for renewal in June 2009.
My question is this: is there a possibility that we will have to pay another CMHC premium when we renew our mortgage, if we have less than 20% equity at renewal?
I'm hoping that our initial premium covers us for the entire life of the mortgage, and not just for the initial term. I just haven't been able to find a definitive answer.
I'd appreciate any insight you can provide.
As I've mentioned in the past, Ms. Loonie and I bought our condo using a CMHC-insured, high-ratio mortgage. We've since paid off our CMHC premium, and are now making progress on the "real" mortgage principal. Our mortgage will be up for renewal in June 2009.
My question is this: is there a possibility that we will have to pay another CMHC premium when we renew our mortgage, if we have less than 20% equity at renewal?
I'm hoping that our initial premium covers us for the entire life of the mortgage, and not just for the initial term. I just haven't been able to find a definitive answer.
I'd appreciate any insight you can provide.
UPDATE
I found the following via Red Flag Deals:http://www.calgarybestmortgage.com/renew.htmlBased on this, it seems that we're insured for the entire life of the mortgage, based on our initial premium. Does that sound right?
Q: When switching my mortgage to a new lender, will I need to pay CMHC insurance fee again? Are there any expenses I need to be aware of?
When switching an insured mortgage, CMHC insurance number will simply be transfered to a new lender at no cost to you. Typically on a mortgage switch lenders will also cover your legal and appraisal expenses for you.
Tuesday, August 28, 2007
Inflation can be your friend.
JLP at AllFinancialMatters has a very interesting post on the impact that inflation has on the true cost of a mortgage. He argues that, because of inflation, the dollars used to make a mortgage payment ten years from now will be worth far less than the dollars used to make a payment today. Therefore, assuming that the amount of the mortgage payment remains constant over those ten years, the cost of the mortgage essentially goes down over time.
This is a great observation, and it has really got me thinking. I was curious what the impact would be on our own mortgage, and found that adjusting for a 3% inflation rate takes our actual cost of borrowing (total payments minus starting principal) from $190K down to $54K. That's a huge difference!
As I played around with these numbers, it occurred to me that this principle can also be used to accelerate a debt paydown. If we were to increase our mortgage payments by 3% each year, we would shorten the life of our mortgage by six years, while further lowering the adjusted cost of borrowing to $44K. Obviously, the challenge is in actually finding that extra 3% each year, but by really making a commitment and developing a sufficiently lean budget, this may very well be manageable.
I'll be looking very seriously at implementing something like this in the new year. I'll let you know how it goes.
This is a great observation, and it has really got me thinking. I was curious what the impact would be on our own mortgage, and found that adjusting for a 3% inflation rate takes our actual cost of borrowing (total payments minus starting principal) from $190K down to $54K. That's a huge difference!
As I played around with these numbers, it occurred to me that this principle can also be used to accelerate a debt paydown. If we were to increase our mortgage payments by 3% each year, we would shorten the life of our mortgage by six years, while further lowering the adjusted cost of borrowing to $44K. Obviously, the challenge is in actually finding that extra 3% each year, but by really making a commitment and developing a sufficiently lean budget, this may very well be manageable.
I'll be looking very seriously at implementing something like this in the new year. I'll let you know how it goes.
Thursday, July 26, 2007
Another Mortgage Milestone...
I posted two weeks ago that we had finally finished paying off the CMHC premium on our mortgage. This meant that the principal on our mortgage was finally below the $316,000 that we "really" borrowed to buy our condo.
Well, the daily interest on the mortgage took our outstanding balance back above $316,000, but with today's payment, we are finally at the point where that will never happen again. From now on, our mortgage balance will do nothing but move down from the $316,000 mark.
This is really just a psychological thing, but it's good to be making real headway on the mortgage.
Well, the daily interest on the mortgage took our outstanding balance back above $316,000, but with today's payment, we are finally at the point where that will never happen again. From now on, our mortgage balance will do nothing but move down from the $316,000 mark.
This is really just a psychological thing, but it's good to be making real headway on the mortgage.
Thursday, July 12, 2007
So long, CMHC
We made our final CMHC payment today.
For those who don't know, CMHC (Canadian Mortgage and Housing Corporation) is the agency that insures "high ratio" mortgages against default. If you have a down payment of less than 25% when you purchase a home in Canada, you pay a premium of 2-4% of the total amount borrowed. I think this is similar to PMI (Private Mortgage Insurance) in the US.
The CMHC amount is usually tacked onto the mortgage amount, and you spend your first year as a homeowner working to pay off that premium, without touching the actual purchase price at all.
We bought our condo last June, and today we paid off the last $66.76 of CMHC, along with $286.22 of the purchase price. This means that, for the first time since we moved, we have actually made real progress on our mortgage.
And it feels good.
For those who don't know, CMHC (Canadian Mortgage and Housing Corporation) is the agency that insures "high ratio" mortgages against default. If you have a down payment of less than 25% when you purchase a home in Canada, you pay a premium of 2-4% of the total amount borrowed. I think this is similar to PMI (Private Mortgage Insurance) in the US.
The CMHC amount is usually tacked onto the mortgage amount, and you spend your first year as a homeowner working to pay off that premium, without touching the actual purchase price at all.
We bought our condo last June, and today we paid off the last $66.76 of CMHC, along with $286.22 of the purchase price. This means that, for the first time since we moved, we have actually made real progress on our mortgage.
And it feels good.
Wednesday, July 11, 2007
Demystifying Mortgage Rates
I'm a die-hard "numbers guy". I've always loved using spreadsheets to lay out and track various scenarios, typically related to personal finance. I like to know exactly what the numbers in my life mean to me. This doesn't mean that I'm particularly good at acting on what the numbers tell me (refer to my total debts in previous posts for proof of this), but it does mean that I'm always "tinkering" with the data in my life.
One thing that has always fascinated me is the tracking of loan payments over time. I had the basic exposure to simple and compound interest calculations in high school, but these calculations almost always focused on a starting principal that remained constant over time. For example, "Sam has $1,000 that earns interest at a rate of 4.0%, compounded monthly. How much money does he have after two years?" The answer to this is very simple ($1,000 x (1 + 0.04) ^ 24 = $2,563.30), because the interest is the only source of change over time. However, when periodic payments, either toward an investment or against a debt, are brought into the picture, the answer gets more complicated, and is harder to express as a single formula (there are, in fact, "simple" formulas that take these payments into account, but their form is not exactly intuitive to the average person).
For every loan I've ever had, I've created a spreadsheet that details, over time, how much interest is accruing from one payment to the next, and how much principal remains over time. These are usually pretty accurate, but when I set up a spreadsheet for my mortgage, I found that my interest calculations were consistently higher than the actual interest charged, resulting in a longer calculated amortization. It turns out that this is due to the way mortgage rates are reported in Canada.
Canadian lenders post mortgage rates that are "compounded semi-annually, not in advance". Well, that clears it all up, doesn't it? It turns out this is actually very simple, but we need to sort out the jargon.
The "compounded semi-annually" part means that the rate is posted assuming that interest will be calculated every six months. The "not in advance" part means that interest is charged after it accrues, so you don't start out your mortgage owing six months' worth of interest. That is, if you have a $100,000 mortgage with a posted rate of 7.0%, then after the first six months, you would see an interest charge of $3,500 ($100,000 x 0.07 / 2). Note that this is actually equivalent to an annual rate of 7.1225% ((1 + 0.07 / 2) ^ 2 - 1), as opposed to the posted 7.0% rate.
In the real world, however, no one pays their mortgage semi-annually; most mortgagees make monthly payments. In the example above, this means that the rate of 7.1225% needs to be converted to monthly compounding, so each month, we would expect an interest charge of 0.575% ((1 + 0.071225) ^ (1 / 12) - 1). Multiplying this rate over twelve months gives us a true effective annual rate of 6.90%. Using this calculated rate, mortgage interest works out to within a few cents of what is actually charged by the lender.
The calculations here may seem a bit confusing, but here is a summary:
I was quite shocked the first time I worked this out, because I could not figure out why lenders would advertise mortgage rates above what they actually end up charging. It turns out that financial institutions are required by law to express their interest rates this way, so that consumers are able to compare "apples to apples", since all lenders are advertising their rates on the "semi-annually, not in advance" scale.
So now you know.
One thing that has always fascinated me is the tracking of loan payments over time. I had the basic exposure to simple and compound interest calculations in high school, but these calculations almost always focused on a starting principal that remained constant over time. For example, "Sam has $1,000 that earns interest at a rate of 4.0%, compounded monthly. How much money does he have after two years?" The answer to this is very simple ($1,000 x (1 + 0.04) ^ 24 = $2,563.30), because the interest is the only source of change over time. However, when periodic payments, either toward an investment or against a debt, are brought into the picture, the answer gets more complicated, and is harder to express as a single formula (there are, in fact, "simple" formulas that take these payments into account, but their form is not exactly intuitive to the average person).
For every loan I've ever had, I've created a spreadsheet that details, over time, how much interest is accruing from one payment to the next, and how much principal remains over time. These are usually pretty accurate, but when I set up a spreadsheet for my mortgage, I found that my interest calculations were consistently higher than the actual interest charged, resulting in a longer calculated amortization. It turns out that this is due to the way mortgage rates are reported in Canada.
Canadian lenders post mortgage rates that are "compounded semi-annually, not in advance". Well, that clears it all up, doesn't it? It turns out this is actually very simple, but we need to sort out the jargon.
The "compounded semi-annually" part means that the rate is posted assuming that interest will be calculated every six months. The "not in advance" part means that interest is charged after it accrues, so you don't start out your mortgage owing six months' worth of interest. That is, if you have a $100,000 mortgage with a posted rate of 7.0%, then after the first six months, you would see an interest charge of $3,500 ($100,000 x 0.07 / 2). Note that this is actually equivalent to an annual rate of 7.1225% ((1 + 0.07 / 2) ^ 2 - 1), as opposed to the posted 7.0% rate.
In the real world, however, no one pays their mortgage semi-annually; most mortgagees make monthly payments. In the example above, this means that the rate of 7.1225% needs to be converted to monthly compounding, so each month, we would expect an interest charge of 0.575% ((1 + 0.071225) ^ (1 / 12) - 1). Multiplying this rate over twelve months gives us a true effective annual rate of 6.90%. Using this calculated rate, mortgage interest works out to within a few cents of what is actually charged by the lender.
The calculations here may seem a bit confusing, but here is a summary:
- R = Annual rate posted by lender
- r = Effective annual rate charged by lender
- r = 12 x (((1 + R / 2) ^ 2) ^ (1 / 12) - 1)
- R = Annual rate posted by lender
- r = Effective annual rate charged by lender
- r = 12 x (((1 + R / 12) ^ 12) ^ (1 / 12) - 1)
- r = 12 x (1 + R / 12 - 1) = R
I was quite shocked the first time I worked this out, because I could not figure out why lenders would advertise mortgage rates above what they actually end up charging. It turns out that financial institutions are required by law to express their interest rates this way, so that consumers are able to compare "apples to apples", since all lenders are advertising their rates on the "semi-annually, not in advance" scale.
So now you know.
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