UK loans: how is monthly pmt determined?

[JoeU2004]

I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of about
0.9489% by NOMINAL(12%,12)/12, which is equivalent to RATE(12,0,-1,1+12%).
In other words, the annual rate is determined by compounding the monthly
rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years would be
about 1060.18, computed by PMT(RATE(12,0,-1,1+12%), 30*12, -108000).

However, three online calculators [*] compute a different payment. The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results in
about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[Bernard Liengme]

I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender to
quote an annual rate that is some how related to a 6-month rate but charged
monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your calculation. As
an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes

 

[trip_to_tokyo]

Hi Joe. I am an Associate of the Chartered Institute of Bankers in London.

The answer to your question would be found in your loan documentation.

All financial insitutions will do this differently but in broad terms the
calculations will be:-

Principal amount outstanding (eg GBP 100,000.00) TIMES the rate of interest
(eg 4%) TIMES the period outstanding (in days) DIVIDED BY 365.

There are many different ways of doing this depending upon the way your loan
is structured.

The only way to be 100% sure of what the bank is charging you (and how they
perform their calculation) is to check your formal loan agreement.

Please hit Yes if my comments have been hekpful to you.

Thanks!

 

[Fred Smith]

Bernard,

Canadian mortgages are compounded semi-annually. Why? Because they are.

Other than that, our mortgages are like any other. Everyone quotes an annual
rate, so do we. You can pay your mortgage monthly, weekly, bi-weekly,
semi-monthly, or any other period that you and the lender agree on.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't have
this protection, paying weekly can actually attract a higher APR than paying
monthly.

Regards,
Fred.

I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender to
quote an annual rate that is some how related to a 6-month rate but
charged monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your calculation.
As an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes
--
Bernard V Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme
remove caps from email

I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about 0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%). In other words, the annual rate is determined by
compounding the monthly rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years would
be about 1060.18, computed by PMT(RATE(12,0,-1,1+12%), 30*12, -108000).

However, three online calculators [*] compute a different payment. The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results in
about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[JoeU2004]

I am an Associate of the Chartered Institute of Bankers in London.

I appreciate your authoritative insights.

All financial insitutions will do this differently but in broad terms the
calculations will be:-
Principal amount outstanding (eg GBP 100,000.00) TIMES the rate of
interest
(eg 4%) TIMES the period outstanding (in days) DIVIDED BY 365.

That might be how interest is calculated per payment period.

My question was: how is the constant periodic (e.g. monthly) payment
calculated, for mortgage loans per se?

In any case, what you describe is not mathematically correct, assuming the
constant periodic payment provided by the aforementioned UK online
calculators.

Consider a loan of 20,000 at 12% with monthly payments over 5 years (i.e. 60
payments). Assume the loan is funded on 12/1/2008, with the first payment
due on 1/1/2009 and on the 1st of each subsequent month. (I am choosing a
simpler example so it is easy to duplicate in a spreadsheet.)

If the payment is calculated according to the aforementioned UK online
calculators, it is about 462.35 per month.

With your method of computing the amount of interest paid each period, using
exact days, the loan is paid off with the 57th payment, not the 60th
payment, and the monthly interest rate varies.

But if the constant monthly interest rate is about 1.1424%, computed by
RATE(60,PMT(12%,5,-20000)/12,-20000) or the equivalent, the loan is
correctly paid off with the 60th payment.

So, is the amount of interest determined as you say; or is it 1.1424% of the
outstanding balance?

I presume that your algorithm above is intended to be a "rule of thumb"
(approximation), and the real constant payment and constant monthly interest
rate are calculated according to the methods used by the UK online
calculators. Right?

Alternatively, Solver or the equivalent could be used to find a constant
payment, namely about 444.90, that reduces the loan to zero in 60 months
using the algorithm exactly as you stated. Is that how UK lenders determine
the payment?

Alternatively, finally, in the US, there is a difference between how
interest per period is calculated for mortgage loans ("closed-end loans")
and for lines of credit and credit cards ("open-end loans"). Does the UK
make a similar distinction, and your description applies to the latter
instead of the former?

PS: FYI, frequently people in these forums ask how to compute the periodic
payment and interest or an annuity schedule for a mortgage loan. We usually
answer them from a US perspective. I usually include a caveat about
Canadian loans, which I am familiar with. I am seeking authoritative
information about UK loans so that I can include a caveat about UK loans as
well. The MS KB article does not agree with the UK online calculators. I
am trying to resolve this discrepancy.


----- original message -----

Hi Joe. I am an Associate of the Chartered Institute of Bankers in London.

The answer to your question would be found in your loan documentation.

All financial insitutions will do this differently but in broad terms the
calculations will be:-

Principal amount outstanding (eg GBP 100,000.00) TIMES the rate of
interest
(eg 4%) TIMES the period outstanding (in days) DIVIDED BY 365.

There are many different ways of doing this depending upon the way your
loan
is structured.

The only way to be 100% sure of what the bank is charging you (and how
they
perform their calculation) is to check your formal loan agreement.

Please hit Yes if my comments have been hekpful to you.

Thanks!

I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about
0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%).
In other words, the annual rate is determined by compounding the monthly
rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years would
be
about 1060.18, computed by PMT(RATE(12,0,-1,1+12%), 30*12, -108000).

However, three online calculators [*] compute a different payment. The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results in
about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[JoeU2004]

When you find the rules, use a website to double check
your calculation. As an ex-Brit I still trust Auntie so
I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

See my endnotes.

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate

Don't confuse APR with annual interest rate.

It is true that in the US and Canada, the APR and annual interest rate are
the same if we ignore front-end and back-end costs ("loan fees") and
periodic fees in addition to principal and interest (e.g. PIM and
"maintenance fees").

But that is apparently not the case for the UK.

I would Google (or Bing) to see if I could find the rules

I could not find authoritative rules with a Google search. That is why I
asking in this forum.

Arguably, this is not exactly an Excel question. I justify posting the
question here because my purpose is to improve my response to FAQs in these
Excel NGs about how to compute period payments and annuity schedules for
mortgage loans.

Wiki and even MS KB articles are not authoritative sources, IMHO, although
sometimes they are a good start.

In fact, considering how the UK APR is computed, I suspect the MS KB article
mistakenly ass-u-me-s that the same method of computation also applies to
the interest rate.

Apparently, it does not, based on the results of three UK online
mortgage calculators that I identified in my initial article in this thread.

In fact, it is that discrepancy that motivated my inquiry, as I explained
in my initial article.


----- original message -----

I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender to
quote an annual rate that is some how related to a 6-month rate but
charged monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your calculation.
As an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes
--
Bernard V Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme
remove caps from email

I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about 0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%). In other words, the annual rate is determined by
compounding the monthly rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years would
be about 1060.18, computed by PMT(RATE(12,0,-1,1+12%), 30*12, -108000).

However, three online calculators [*] compute a different payment. The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results in
about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[JoeU2004]

Canadian mortgages are compounded semi-annually

That is indeed the terminology that Canadians use. But it is incorrect --
and misleading, IMHO.

If I compound a daily rate for 30 days, then multiply by 12 to get an annual
rate (30/360 basis), would you say that the rate is "compounded monthly"?

Rhetorical question. Of course you wouldn't. I'm sure you know that
"compounded monthly" means (1+r)^12-1.

Likewise, the Canadian rate is not "compounded semi-annually" -- (1+r)^2-1.

Instead, the Canadian rate is "compounded monthly semi-annually" or
"compounded monthly over 6 months twice a year" or something like that.
That is, it is ((1+r)^6-1)*2.

That is corroborated by the aforementioned MS KB article and Canadian online
mortgage calculators.

Well, that's for a loan with monthly payments. The annual rate for a
Canadian loan with weekly payments, for example, is the weekly rate
compounded over 26 weeks, then multiplied by 2. So it is "compounded weekly
semi-annually".

So we can see why Canadians settle for the incorrect term "compounded
semi-annually". It is a mouthful to say "compounded F semi-annually, where
F is the payment frequency", which is the correct term.

While the compounding period is somewhat annoying, the
advantage is the lender can't play games with the rate.

Horse-pucky! Lenders are just as adept at hiring financial mathematicians
as anyone else.

A lender decides what ROI he needs, considering in actuarial factors such as
foreclosure and other bad debt risks, expected life of a loan (usually less
than full term), etc and considering in market factors such as competition,
what the market will bear, etc.

Then he reverse-engineers the formula -- any formula -- to arrive at a
periodic rate.

In other counties that don't have this protection,
paying weekly can actually attract a higher APR than
paying monthly.

And somehow the Canadian method prevents that?! Please demonstrate.

In the US, the APR is a nominal rate. So, a 12% APR loan with weekly
payments means that the weekly rate is 12%/52, and a 12% APR loan with
monthly payments means that the monthly rate is 12%/12. The APR is 12%
regardless of the payment frequency.

The UK APR is a compounded rate. So, a 12% APR loan with weekly payments
means that the week rate is (1+12%)^(1/52)-1, and a 12% APR loan with
monthly payments means that the monthly rate is (1+12%)^(1/12)-1. Again,
the APR is 12% regardless of the payment frequency.

Note: In Canada and the US, the only difference between APR and annual
interest rate is the amount of funding and perhaps the amount of periodic
payments that are used in calculation. Ignoring front-end and back-end
costs ("loan fees") and periodic fees other than principal and interest
(PMI, period maintenance fees, etc), the APR and annual interest rate are
the same. This is true for both Canada and the US. It is not true for the
UK.

Fred might be thinking that a UK loan with an annual interest rate of 12% is
about 12.88% APR for weekly payments and about 12.82% APR for monthly
payments. But I would not say the methodology "attracts" a higher APR for
lack of protection against it. It is simply a mathematical consequence of
how the APR is computed in the UK. So what?

(Note: The computation in the previous paragraph presumes an answer to my
question which might be incorrect, according to "Trip's" first response.)


----- original message -----

Bernard,

Canadian mortgages are compounded semi-annually. Why? Because they are.

Other than that, our mortgages are like any other. Everyone quotes an
annual rate, so do we. You can pay your mortgage monthly, weekly,
bi-weekly, semi-monthly, or any other period that you and the lender agree
on.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't have
this protection, paying weekly can actually attract a higher APR than
paying monthly.

Regards,
Fred.

I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender to
quote an annual rate that is some how related to a 6-month rate but
charged monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your calculation.
As an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes
--
Bernard V Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme
remove caps from email

I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about 0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%). In other words, the annual rate is determined by
compounding the monthly rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years
would be about 1060.18, computed by PMT(RATE(12,0,-1,1+12%),
30*12, -108000).

However, three online calculators [*] compute a different payment. The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results
in about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[trip_to_tokyo]

Joe, very briefly, as my time is very limited.

My comments were intended as a rough guide only.

If you want to rig up a spreadhseet to check what the loan giver is doing it
can be done but it is not a straighforward task.

I would say that the starting point for such an endeavour must be the loan
documentation itself which will tell you exactly how the lender is
calculating interest. If you do this you should be able to come close to what
the lender is doing. Foe accuracy I would work to 20 decimal places.

I am an Associate of the Chartered Institute of Bankers in London.

I appreciate your authoritative insights.

All financial insitutions will do this differently but in broad terms the
calculations will be:-
Principal amount outstanding (eg GBP 100,000.00) TIMES the rate of
interest
(eg 4%) TIMES the period outstanding (in days) DIVIDED BY 365.

That might be how interest is calculated per payment period.

My question was: how is the constant periodic (e.g. monthly) payment
calculated, for mortgage loans per se?

In any case, what you describe is not mathematically correct, assuming the
constant periodic payment provided by the aforementioned UK online
calculators.

Consider a loan of 20,000 at 12% with monthly payments over 5 years (i.e. 60
payments). Assume the loan is funded on 12/1/2008, with the first payment
due on 1/1/2009 and on the 1st of each subsequent month. (I am choosing a
simpler example so it is easy to duplicate in a spreadsheet.)

If the payment is calculated according to the aforementioned UK online
calculators, it is about 462.35 per month.

With your method of computing the amount of interest paid each period, using
exact days, the loan is paid off with the 57th payment, not the 60th
payment, and the monthly interest rate varies.

But if the constant monthly interest rate is about 1.1424%, computed by
RATE(60,PMT(12%,5,-20000)/12,-20000) or the equivalent, the loan is
correctly paid off with the 60th payment.

So, is the amount of interest determined as you say; or is it 1.1424% of the
outstanding balance?

I presume that your algorithm above is intended to be a "rule of thumb"
(approximation), and the real constant payment and constant monthly interest
rate are calculated according to the methods used by the UK online
calculators. Right?

Alternatively, Solver or the equivalent could be used to find a constant
payment, namely about 444.90, that reduces the loan to zero in 60 months
using the algorithm exactly as you stated. Is that how UK lenders determine
the payment?

Alternatively, finally, in the US, there is a difference between how
interest per period is calculated for mortgage loans ("closed-end loans")
and for lines of credit and credit cards ("open-end loans"). Does the UK
make a similar distinction, and your description applies to the latter
instead of the former?

PS: FYI, frequently people in these forums ask how to compute the periodic
payment and interest or an annuity schedule for a mortgage loan. We usually
answer them from a US perspective. I usually include a caveat about
Canadian loans, which I am familiar with. I am seeking authoritative
information about UK loans so that I can include a caveat about UK loans as
well. The MS KB article does not agree with the UK online calculators. I
am trying to resolve this discrepancy.


----- original message -----

Hi Joe. I am an Associate of the Chartered Institute of Bankers in London.

The answer to your question would be found in your loan documentation.

All financial insitutions will do this differently but in broad terms the
calculations will be:-

Principal amount outstanding (eg GBP 100,000.00) TIMES the rate of
interest
(eg 4%) TIMES the period outstanding (in days) DIVIDED BY 365.

There are many different ways of doing this depending upon the way your
loan
is structured.

The only way to be 100% sure of what the bank is charging you (and how
they
perform their calculation) is to check your formal loan agreement.

Please hit Yes if my comments have been hekpful to you.

Thanks!

I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about
0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%).
In other words, the annual rate is determined by compounding the monthly
rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years would
be
about 1060.18, computed by PMT(RATE(12,0,-1,1+12%), 30*12, -108000).

However, three online calculators [*] compute a different payment. The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results in
about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[Fred Smith]

"And somehow the Canadian method prevents that?! Please demonstrate."

OK. Let's take a $1,000,000 at 6% and calculate the future value using
different periodic rates (using your formulae to calculate the rate which I
agree is correct, although I've simplified the Canadian one).
US, monthly, rate = 6%/12, FV = 6,022,575.21
US, weekly, rate = 6%/52, FV = 6,043,373.22
UK, monthly, rate = (1+6%)^(1/12)-1, FV = 5,743,491.17
UK, weekly, rate = (1+6%)^(1/52)-1, FV = 5,743,491.17
Cdn, monthly, rate = (1+6%/2)^(2/12)-1, FV = 5,891,603.10
Cdn, weekly, rate = (1+6%/2)^(2/52)-1, FV = 5,891,603.10

In Canada and the UK, the frequency has no impact on future value. For a
mortgage, that means the payment frequency will not affect the interest you
are charged.

In the US, frequency does impact future value, meaning you're charged more
interest on your mortgage the more frequently you pay.

Our legislation requiring mortgages to be "compounded semi-annually not in
advance" is annoying, I agree, but we have to have some quirks, don't we?

Regards,
Fred.

Canadian mortgages are compounded semi-annually

That is indeed the terminology that Canadians use. But it is incorrect --
and misleading, IMHO.

If I compound a daily rate for 30 days, then multiply by 12 to get an
annual
rate (30/360 basis), would you say that the rate is "compounded monthly"?

Rhetorical question. Of course you wouldn't. I'm sure you know that
"compounded monthly" means (1+r)^12-1.

Likewise, the Canadian rate is not "compounded semi-annually" --
(1+r)^2-1.

Instead, the Canadian rate is "compounded monthly semi-annually" or
"compounded monthly over 6 months twice a year" or something like that.
That is, it is ((1+r)^6-1)*2.

That is corroborated by the aforementioned MS KB article and Canadian
online
mortgage calculators.

Well, that's for a loan with monthly payments. The annual rate for a
Canadian loan with weekly payments, for example, is the weekly rate
compounded over 26 weeks, then multiplied by 2. So it is "compounded
weekly
semi-annually".

So we can see why Canadians settle for the incorrect term "compounded
semi-annually". It is a mouthful to say "compounded F semi-annually,
where
F is the payment frequency", which is the correct term.

While the compounding period is somewhat annoying, the
advantage is the lender can't play games with the rate.

Horse-pucky! Lenders are just as adept at hiring financial mathematicians
as anyone else.

A lender decides what ROI he needs, considering in actuarial factors such
as
foreclosure and other bad debt risks, expected life of a loan (usually
less
than full term), etc and considering in market factors such as
competition,
what the market will bear, etc.

Then he reverse-engineers the formula -- any formula -- to arrive at a
periodic rate.

In other counties that don't have this protection,
paying weekly can actually attract a higher APR than
paying monthly.

And somehow the Canadian method prevents that?! Please demonstrate.

In the US, the APR is a nominal rate. So, a 12% APR loan with weekly
payments means that the weekly rate is 12%/52, and a 12% APR loan with
monthly payments means that the monthly rate is 12%/12. The APR is 12%
regardless of the payment frequency.

The UK APR is a compounded rate. So, a 12% APR loan with weekly payments
means that the week rate is (1+12%)^(1/52)-1, and a 12% APR loan with
monthly payments means that the monthly rate is (1+12%)^(1/12)-1. Again,
the APR is 12% regardless of the payment frequency.

Note: In Canada and the US, the only difference between APR and annual
interest rate is the amount of funding and perhaps the amount of periodic
payments that are used in calculation. Ignoring front-end and back-end
costs ("loan fees") and periodic fees other than principal and interest
(PMI, period maintenance fees, etc), the APR and annual interest rate are
the same. This is true for both Canada and the US. It is not true for
the
UK.

Fred might be thinking that a UK loan with an annual interest rate of 12%
is
about 12.88% APR for weekly payments and about 12.82% APR for monthly
payments. But I would not say the methodology "attracts" a higher APR for
lack of protection against it. It is simply a mathematical consequence of
how the APR is computed in the UK. So what?

(Note: The computation in the previous paragraph presumes an answer to my
question which might be incorrect, according to "Trip's" first response.)


----- original message -----

Bernard,

Canadian mortgages are compounded semi-annually. Why? Because they are.

Other than that, our mortgages are like any other. Everyone quotes an
annual rate, so do we. You can pay your mortgage monthly, weekly,
bi-weekly, semi-monthly, or any other period that you and the lender
agree
on.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't have
this protection, paying weekly can actually attract a higher APR than
paying monthly.

Regards,
Fred.

I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender to
quote an annual rate that is some how related to a 6-month rate but
charged monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your calculation.
As an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes
--
Bernard V Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme
remove caps from email


I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about 0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%). In other words, the annual rate is determined by
compounding the monthly rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years
would be about 1060.18, computed by PMT(RATE(12,0,-1,1+12%),
30*12, -108000).

However, three online calculators [*] compute a different payment. The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results
in about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[Bob I]

I think you have it backward. IF you reduce the principal more
frequently you will pay LESS interest not MORE. What you are calculating
is the interest RECEIVED on a FIXED amount of principal based on the
compounding frequency. This isn't applicable to mortgages.

"And somehow the Canadian method prevents that?! Please demonstrate."

OK. Let's take a $1,000,000 at 6% and calculate the future value using
different periodic rates (using your formulae to calculate the rate
which I agree is correct, although I've simplified the Canadian one).
US, monthly, rate = 6%/12, FV = 6,022,575.21
US, weekly, rate = 6%/52, FV = 6,043,373.22
UK, monthly, rate = (1+6%)^(1/12)-1, FV = 5,743,491.17
UK, weekly, rate = (1+6%)^(1/52)-1, FV = 5,743,491.17
Cdn, monthly, rate = (1+6%/2)^(2/12)-1, FV = 5,891,603.10
Cdn, weekly, rate = (1+6%/2)^(2/52)-1, FV = 5,891,603.10

In Canada and the UK, the frequency has no impact on future value. For a
mortgage, that means the payment frequency will not affect the interest
you are charged.

In the US, frequency does impact future value, meaning you're charged
more interest on your mortgage the more frequently you pay.

Our legislation requiring mortgages to be "compounded semi-annually not
in advance" is annoying, I agree, but we have to have some quirks, don't
we?

Regards,
Fred.

Canadian mortgages are compounded semi-annually

That is indeed the terminology that Canadians use. But it is
incorrect --
and misleading, IMHO.

If I compound a daily rate for 30 days, then multiply by 12 to get an
annual
rate (30/360 basis), would you say that the rate is "compounded monthly"?

Rhetorical question. Of course you wouldn't. I'm sure you know that
"compounded monthly" means (1+r)^12-1.

Likewise, the Canadian rate is not "compounded semi-annually" --
(1+r)^2-1.

Instead, the Canadian rate is "compounded monthly semi-annually" or
"compounded monthly over 6 months twice a year" or something like that.
That is, it is ((1+r)^6-1)*2.

That is corroborated by the aforementioned MS KB article and Canadian
online
mortgage calculators.

Well, that's for a loan with monthly payments. The annual rate for a
Canadian loan with weekly payments, for example, is the weekly rate
compounded over 26 weeks, then multiplied by 2. So it is "compounded
weekly
semi-annually".

So we can see why Canadians settle for the incorrect term "compounded
semi-annually". It is a mouthful to say "compounded F semi-annually,
where
F is the payment frequency", which is the correct term.

While the compounding period is somewhat annoying, the
advantage is the lender can't play games with the rate.

Horse-pucky! Lenders are just as adept at hiring financial
mathematicians
as anyone else.

A lender decides what ROI he needs, considering in actuarial factors
such as
foreclosure and other bad debt risks, expected life of a loan (usually
less
than full term), etc and considering in market factors such as
competition,
what the market will bear, etc.

Then he reverse-engineers the formula -- any formula -- to arrive at a
periodic rate.

In other counties that don't have this protection,
paying weekly can actually attract a higher APR than
paying monthly.

And somehow the Canadian method prevents that?! Please demonstrate.

In the US, the APR is a nominal rate. So, a 12% APR loan with weekly
payments means that the weekly rate is 12%/52, and a 12% APR loan with
monthly payments means that the monthly rate is 12%/12. The APR is 12%
regardless of the payment frequency.

The UK APR is a compounded rate. So, a 12% APR loan with weekly payments
means that the week rate is (1+12%)^(1/52)-1, and a 12% APR loan with
monthly payments means that the monthly rate is (1+12%)^(1/12)-1. Again,
the APR is 12% regardless of the payment frequency.

Note: In Canada and the US, the only difference between APR and annual
interest rate is the amount of funding and perhaps the amount of periodic
payments that are used in calculation. Ignoring front-end and back-end
costs ("loan fees") and periodic fees other than principal and interest
(PMI, period maintenance fees, etc), the APR and annual interest rate are
the same. This is true for both Canada and the US. It is not true
for the
UK.

Fred might be thinking that a UK loan with an annual interest rate of
12% is
about 12.88% APR for weekly payments and about 12.82% APR for monthly
payments. But I would not say the methodology "attracts" a higher APR
for
lack of protection against it. It is simply a mathematical
consequence of
how the APR is computed in the UK. So what?

(Note: The computation in the previous paragraph presumes an answer
to my
question which might be incorrect, according to "Trip's" first response.)


----- original message -----

Bernard,

Canadian mortgages are compounded semi-annually. Why? Because they are.

Other than that, our mortgages are like any other. Everyone quotes an
annual rate, so do we. You can pay your mortgage monthly, weekly,
bi-weekly, semi-monthly, or any other period that you and the lender
agree
on.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't
have
this protection, paying weekly can actually attract a higher APR than
paying monthly.

Regards,
Fred.


I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender to
quote an annual rate that is some how related to a 6-month rate but
charged monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your
calculation.
As an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes
--
Bernard V Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme
remove caps from email



I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your
mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about 0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%). In other words, the annual rate is determined by
compounding the monthly rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years
would be about 1060.18, computed by PMT(RATE(12,0,-1,1+12%),
30*12, -108000).

However, three online calculators [*] compute a different payment.
The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results
in about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[JoeU2004]

OK. Let's take a $1,000,000 at 6% and calculate the
future value using different periodic rates
[...]
US, monthly, rate = 6%/12, FV = 6,022,575.21
US, weekly, rate = 6%/52, FV = 6,043,373.22

First, you are confusing the mechanics for a fixed-rate investment (e.g.
savings) with the mechanics for a mortgage loan.

Second, your examples incorrectly compute the UK periodic rate, basing it on
an APR instead of interest rate, if we are to believe the UK online mortgage
calculators.

Perhaps your intention was to show the following for a 30-year loan of
1,000,000 at 6%. Actual amounts are rounded. UK #a is based on the
aforementioned UK online mortgage calculators; UK #b is based on the
aforementioned MS KB article.

1. US monthly rate: 0.5000% 6%/12
monthly payment: 5,995.51
total interest: 1,158,381.89

2. US weekly rate: 0.1154% 6%/52
weekly payment: 1,382.63
total interest: 1,156,903.98

3a. UK monthly rate: 0.5076% RATE(360,PMT(...),-1000000)
monthly payment: 6,054.08 PMT(6%,30,-1000000)/12
total interest: 1,179,467.34

b. UK monthly rate: 0.4868% (1+6%)^(1/12)-1
monthly payment: 5,893.70
total interest: 1,121,733.50

4a. UK weekly rate: 0.1173% Solver [*]
monthly payment: 1,397.09 PMT(6%,30,-1000000)/52
total interest: 1,179,467.34

[*] RATE(1560,PMT(...),-1000000,0.1173%) fails!

b. UK weekly rate: 0.1121% (1+6%)^(1/52)-1
monthly payment: 1,357.55
total interest: 1,117,772.69

5. CA monthly rate: 0.4939% (1+6%/2)^(1/6)-1
monthly payment: 5,948.23
total interest: 1,141,364.31

6. CA weekly rate: 0.1138% (1+6%/2)^(1/26)-1
monthly payment: 1,370.07
total interest: 1,137,308.66

But this shows that for both the US and Canada, the total interest is
affected the payment frequency. The Canadian method of determining annual
interest rate by so-called "compounding semi-annually" offers no
"protection" or less "attraction" whatsoever.

The same is true for the UK if the annual interest rate is (truly)
compounded by the payment frequency. However, if the UK periodic payment is
calculated according to the UK online calculators, the UK total interest is
unaffected by payment frequency. (By definition; no surprise.)

In any case, that was not the point you made to which I responded as you
quoted above.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't have
this protection, paying weekly can actually attract a higher APR than
paying monthly.

You were making a point about "attracting" a higher APR.

Note: Here, we are talking about APR, not necessarily interest rate.

As I have said, the US APR is not affected by the payment frequency, any
more than the Canadian APR. In both case, the APR is the annual interest
rate, if we ignore loan fees and period fees other than principal and
interest.

As for the UK, the APR is indeed affected by the payment frequency, if we
believe the MS KB article. But that is just a mathematical fact. I see no
sinister "attraction" in that and nothing to be "protected" from.

I guess I really do not understand the point that you are trying to make
either by the original "attraction" statement or by your follow-up here.


----- original message -----

"And somehow the Canadian method prevents that?! Please demonstrate."

OK. Let's take a $1,000,000 at 6% and calculate the future value using
different periodic rates (using your formulae to calculate the rate which
I agree is correct, although I've simplified the Canadian one).
US, monthly, rate = 6%/12, FV = 6,022,575.21
US, weekly, rate = 6%/52, FV = 6,043,373.22
UK, monthly, rate = (1+6%)^(1/12)-1, FV = 5,743,491.17
UK, weekly, rate = (1+6%)^(1/52)-1, FV = 5,743,491.17
Cdn, monthly, rate = (1+6%/2)^(2/12)-1, FV = 5,891,603.10
Cdn, weekly, rate = (1+6%/2)^(2/52)-1, FV = 5,891,603.10

In Canada and the UK, the frequency has no impact on future value. For a
mortgage, that means the payment frequency will not affect the interest
you are charged.

In the US, frequency does impact future value, meaning you're charged more
interest on your mortgage the more frequently you pay.

Our legislation requiring mortgages to be "compounded semi-annually not in
advance" is annoying, I agree, but we have to have some quirks, don't we?

Regards,
Fred.

Canadian mortgages are compounded semi-annually

That is indeed the terminology that Canadians use. But it is
incorrect --
and misleading, IMHO.

If I compound a daily rate for 30 days, then multiply by 12 to get an
annual
rate (30/360 basis), would you say that the rate is "compounded monthly"?

Rhetorical question. Of course you wouldn't. I'm sure you know that
"compounded monthly" means (1+r)^12-1.

Likewise, the Canadian rate is not "compounded semi-annually" --
(1+r)^2-1.

Instead, the Canadian rate is "compounded monthly semi-annually" or
"compounded monthly over 6 months twice a year" or something like that.
That is, it is ((1+r)^6-1)*2.

That is corroborated by the aforementioned MS KB article and Canadian
online
mortgage calculators.

Well, that's for a loan with monthly payments. The annual rate for a
Canadian loan with weekly payments, for example, is the weekly rate
compounded over 26 weeks, then multiplied by 2. So it is "compounded
weekly
semi-annually".

So we can see why Canadians settle for the incorrect term "compounded
semi-annually". It is a mouthful to say "compounded F semi-annually,
where
F is the payment frequency", which is the correct term.

While the compounding period is somewhat annoying, the
advantage is the lender can't play games with the rate.

Horse-pucky! Lenders are just as adept at hiring financial
mathematicians
as anyone else.

A lender decides what ROI he needs, considering in actuarial factors such
as
foreclosure and other bad debt risks, expected life of a loan (usually
less
than full term), etc and considering in market factors such as
competition,
what the market will bear, etc.

Then he reverse-engineers the formula -- any formula -- to arrive at a
periodic rate.

In other counties that don't have this protection,
paying weekly can actually attract a higher APR than
paying monthly.

And somehow the Canadian method prevents that?! Please demonstrate.

In the US, the APR is a nominal rate. So, a 12% APR loan with weekly
payments means that the weekly rate is 12%/52, and a 12% APR loan with
monthly payments means that the monthly rate is 12%/12. The APR is 12%
regardless of the payment frequency.

The UK APR is a compounded rate. So, a 12% APR loan with weekly payments
means that the week rate is (1+12%)^(1/52)-1, and a 12% APR loan with
monthly payments means that the monthly rate is (1+12%)^(1/12)-1. Again,
the APR is 12% regardless of the payment frequency.

Note: In Canada and the US, the only difference between APR and annual
interest rate is the amount of funding and perhaps the amount of periodic
payments that are used in calculation. Ignoring front-end and back-end
costs ("loan fees") and periodic fees other than principal and interest
(PMI, period maintenance fees, etc), the APR and annual interest rate are
the same. This is true for both Canada and the US. It is not true for
the
UK.

Fred might be thinking that a UK loan with an annual interest rate of 12%
is
about 12.88% APR for weekly payments and about 12.82% APR for monthly
payments. But I would not say the methodology "attracts" a higher APR
for
lack of protection against it. It is simply a mathematical consequence
of
how the APR is computed in the UK. So what?

(Note: The computation in the previous paragraph presumes an answer to
my
question which might be incorrect, according to "Trip's" first response.)


----- original message -----

Bernard,

Canadian mortgages are compounded semi-annually. Why? Because they are.

Other than that, our mortgages are like any other. Everyone quotes an
annual rate, so do we. You can pay your mortgage monthly, weekly,
bi-weekly, semi-monthly, or any other period that you and the lender
agree
on.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't
have
this protection, paying weekly can actually attract a higher APR than
paying monthly.

Regards,
Fred.

I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender to
quote an annual rate that is some how related to a 6-month rate but
charged monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your
calculation.
As an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes
--
Bernard V Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme
remove caps from email


I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your
mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about 0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%). In other words, the annual rate is determined by
compounding the monthly rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years
would be about 1060.18, computed by PMT(RATE(12,0,-1,1+12%),
30*12, -108000).

However, three online calculators [*] compute a different payment.
The
monthly payment is computed by PMT(12%, 30, -108000)/12, which results
in about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html

 

[JoeU2004]

Errata....

4a. UK weekly rate: 0.1173% Solver [*]
[....]
[*] RATE(1560,PMT(...),-1000000,0.1173%) fails!

Typo! RATE(1560,PMT(...),-1000000,0,0,0.11%) works fine. Even a guess of
1%.


----- original message -----

OK. Let's take a $1,000,000 at 6% and calculate the
future value using different periodic rates
[...]
US, monthly, rate = 6%/12, FV = 6,022,575.21
US, weekly, rate = 6%/52, FV = 6,043,373.22

First, you are confusing the mechanics for a fixed-rate investment (e.g.
savings) with the mechanics for a mortgage loan.

Second, your examples incorrectly compute the UK periodic rate, basing it
on an APR instead of interest rate, if we are to believe the UK online
mortgage calculators.

Perhaps your intention was to show the following for a 30-year loan of
1,000,000 at 6%. Actual amounts are rounded. UK #a is based on the
aforementioned UK online mortgage calculators; UK #b is based on the
aforementioned MS KB article.

1. US monthly rate: 0.5000% 6%/12
monthly payment: 5,995.51
total interest: 1,158,381.89

2. US weekly rate: 0.1154% 6%/52
weekly payment: 1,382.63
total interest: 1,156,903.98

3a. UK monthly rate: 0.5076% RATE(360,PMT(...),-1000000)
monthly payment: 6,054.08 PMT(6%,30,-1000000)/12
total interest: 1,179,467.34

b. UK monthly rate: 0.4868% (1+6%)^(1/12)-1
monthly payment: 5,893.70
total interest: 1,121,733.50

4a. UK weekly rate: 0.1173% Solver [*]
monthly payment: 1,397.09 PMT(6%,30,-1000000)/52
total interest: 1,179,467.34

[*] RATE(1560,PMT(...),-1000000,0.1173%) fails!

b. UK weekly rate: 0.1121% (1+6%)^(1/52)-1
monthly payment: 1,357.55
total interest: 1,117,772.69

5. CA monthly rate: 0.4939% (1+6%/2)^(1/6)-1
monthly payment: 5,948.23
total interest: 1,141,364.31

6. CA weekly rate: 0.1138% (1+6%/2)^(1/26)-1
monthly payment: 1,370.07
total interest: 1,137,308.66

But this shows that for both the US and Canada, the total interest is
affected the payment frequency. The Canadian method of determining annual
interest rate by so-called "compounding semi-annually" offers no
"protection" or less "attraction" whatsoever.

The same is true for the UK if the annual interest rate is (truly)
compounded by the payment frequency. However, if the UK periodic payment
is calculated according to the UK online calculators, the UK total
interest is unaffected by payment frequency. (By definition; no
surprise.)

In any case, that was not the point you made to which I responded as you
quoted above.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't have
this protection, paying weekly can actually attract a higher APR than
paying monthly.

You were making a point about "attracting" a higher APR.

Note: Here, we are talking about APR, not necessarily interest rate.

As I have said, the US APR is not affected by the payment frequency, any
more than the Canadian APR. In both case, the APR is the annual interest
rate, if we ignore loan fees and period fees other than principal and
interest.

As for the UK, the APR is indeed affected by the payment frequency, if we
believe the MS KB article. But that is just a mathematical fact. I see
no sinister "attraction" in that and nothing to be "protected" from.

I guess I really do not understand the point that you are trying to make
either by the original "attraction" statement or by your follow-up here.


----- original message -----

"And somehow the Canadian method prevents that?! Please demonstrate."

OK. Let's take a $1,000,000 at 6% and calculate the future value using
different periodic rates (using your formulae to calculate the rate which
I agree is correct, although I've simplified the Canadian one).
US, monthly, rate = 6%/12, FV = 6,022,575.21
US, weekly, rate = 6%/52, FV = 6,043,373.22
UK, monthly, rate = (1+6%)^(1/12)-1, FV = 5,743,491.17
UK, weekly, rate = (1+6%)^(1/52)-1, FV = 5,743,491.17
Cdn, monthly, rate = (1+6%/2)^(2/12)-1, FV = 5,891,603.10
Cdn, weekly, rate = (1+6%/2)^(2/52)-1, FV = 5,891,603.10

In Canada and the UK, the frequency has no impact on future value. For a
mortgage, that means the payment frequency will not affect the interest
you are charged.

In the US, frequency does impact future value, meaning you're charged
more interest on your mortgage the more frequently you pay.

Our legislation requiring mortgages to be "compounded semi-annually not
in advance" is annoying, I agree, but we have to have some quirks, don't
we?

Regards,
Fred.

Canadian mortgages are compounded semi-annually

That is indeed the terminology that Canadians use. But it is
incorrect --
and misleading, IMHO.

If I compound a daily rate for 30 days, then multiply by 12 to get an
annual
rate (30/360 basis), would you say that the rate is "compounded
monthly"?

Rhetorical question. Of course you wouldn't. I'm sure you know that
"compounded monthly" means (1+r)^12-1.

Likewise, the Canadian rate is not "compounded semi-annually" --
(1+r)^2-1.

Instead, the Canadian rate is "compounded monthly semi-annually" or
"compounded monthly over 6 months twice a year" or something like that.
That is, it is ((1+r)^6-1)*2.

That is corroborated by the aforementioned MS KB article and Canadian
online
mortgage calculators.

Well, that's for a loan with monthly payments. The annual rate for a
Canadian loan with weekly payments, for example, is the weekly rate
compounded over 26 weeks, then multiplied by 2. So it is "compounded
weekly
semi-annually".

So we can see why Canadians settle for the incorrect term "compounded
semi-annually". It is a mouthful to say "compounded F semi-annually,
where
F is the payment frequency", which is the correct term.


While the compounding period is somewhat annoying, the
advantage is the lender can't play games with the rate.

Horse-pucky! Lenders are just as adept at hiring financial
mathematicians
as anyone else.

A lender decides what ROI he needs, considering in actuarial factors
such as
foreclosure and other bad debt risks, expected life of a loan (usually
less
than full term), etc and considering in market factors such as
competition,
what the market will bear, etc.

Then he reverse-engineers the formula -- any formula -- to arrive at a
periodic rate.


In other counties that don't have this protection,
paying weekly can actually attract a higher APR than
paying monthly.

And somehow the Canadian method prevents that?! Please demonstrate.

In the US, the APR is a nominal rate. So, a 12% APR loan with weekly
payments means that the weekly rate is 12%/52, and a 12% APR loan with
monthly payments means that the monthly rate is 12%/12. The APR is 12%
regardless of the payment frequency.

The UK APR is a compounded rate. So, a 12% APR loan with weekly
payments
means that the week rate is (1+12%)^(1/52)-1, and a 12% APR loan with
monthly payments means that the monthly rate is (1+12%)^(1/12)-1.
Again,
the APR is 12% regardless of the payment frequency.

Note: In Canada and the US, the only difference between APR and annual
interest rate is the amount of funding and perhaps the amount of
periodic
payments that are used in calculation. Ignoring front-end and back-end
costs ("loan fees") and periodic fees other than principal and interest
(PMI, period maintenance fees, etc), the APR and annual interest rate
are
the same. This is true for both Canada and the US. It is not true for
the
UK.

Fred might be thinking that a UK loan with an annual interest rate of
12% is
about 12.88% APR for weekly payments and about 12.82% APR for monthly
payments. But I would not say the methodology "attracts" a higher APR
for
lack of protection against it. It is simply a mathematical consequence
of
how the APR is computed in the UK. So what?

(Note: The computation in the previous paragraph presumes an answer to
my
question which might be incorrect, according to "Trip's" first
response.)


----- original message -----

Bernard,

Canadian mortgages are compounded semi-annually. Why? Because they are.

Other than that, our mortgages are like any other. Everyone quotes an
annual rate, so do we. You can pay your mortgage monthly, weekly,
bi-weekly, semi-monthly, or any other period that you and the lender
agree
on.

While the compounding period is somewhat annoying, the advantage is the
lender can't play games with the rate. In other counties that don't
have
this protection, paying weekly can actually attract a higher APR than
paying monthly.

Regards,
Fred.

I would Google (or Bing) to see if I could find the rules
Do not go by the US rules. For example, Canadian law requires lender
to
quote an annual rate that is some how related to a 6-month rate but
charged monthly!

I entered: uk apr "monthly rate" and this seemed useful
http://en.wikipedia.org/wiki/Annual_percentage_rate


When you find the rules, use a website to double check your
calculation.
As an ex-Brit I still trust Auntie so I would go to
http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

best wishes
--
Bernard V Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme
remove caps from email


I would like to hear from UK readers.

How do lenders actually determine the monthly payment for your
mortgage
loan?

According to http://support.microsoft.com/kb/294396/en-us , an annual
interest rate of 12%, for example, is converted to a monthly rate of
about 0.9489% by NOMINAL(12%,12)/12, which is equivalent to
RATE(12,0,-1,1+12%). In other words, the annual rate is determined by
compounding the monthly rate.

Ergo, the monthly payment on a loan of 108,000 at 12% over 30 years
would be about 1060.18, computed by PMT(RATE(12,0,-1,1+12%),
30*12, -108000).

However, three online calculators [*] compute a different payment.
The
monthly payment is computed by PMT(12%, 30, -108000)/12, which
results
in about 1117.29.

That has an effective monthly interest rate of RATE(30*12,
PMT(12%,30,-108000)/12, -108000), which is about 1.0064%.


End notes
---------

[*] Three online calculators:

http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

http://www.cml.org.uk/cml/consumers/calculator/mortcalculator

http://www.mortgages.co.uk/calculator/mortgage_calculator.html