How to do UK mortgage math?

[joeu2004]

Consider a 15-year UK loan of 100,000 (British pounds) at 6% with
monthly payments. How is the monthly payment amount computed? How is
the monthly interest amount computed in an amortization schedule?

(And can someone point me to the UK (or High Street Bank) equivalent
of the US Truth in Lending regulations/guidelines online? I thought I
found them for myself some time ago. But I cannot find them now.)

One online source [1] computes the monthly payment by PMT(6%, 180,
-100000)/12, which is about 858.02 (must be rounded). That agrees
with an independent online UK mortgage calculator [2].

Based on that, I might think that the monthly interest rate is
RATE(180, 858.02, -100000), which is about 0.521746%. Thus, I might
compute monthly interest by B1*RATE(...), where B1 is the previous
period's ending balance (initially 100000). That works out to about
521.75 for the first month.

I have couple problems with those conclusions.

First, the same online UK mortgage calculator [2] computes a monthly
payment of 500 for an interest-only mortgage for the same loan terms.
That would suggest that the monthly rate is simply 6%/12, or
0.500000%.

Second, in another thread, the OP says that UK mortgage interest is
"calculated daily and added monthly", and that the daily interest is
compounded. Is that correct?

If that is correct, how is the daily rate computed?

Ostensibly, it might be r/d (simple interest) or (1+r)^(1/d)-1
(compound interest), where "r" is the monthly rate and "d" is the
number of days in the month (assuming on-time payments). But that
would mean the daily rate is non-uniform. Is it really?

Alternatively, the daily rate might be 6%/365. (Or some other uniform
rate?)

Either way, that seems inconsistent with the way the monthly payment
is computed.


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Endnotes

[1] "Mortgage repayment tables" link on http://www.cml.org.uk/cml/consumers/calculator
..

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

 

[joeu2004]

Consider a 15-year UK loan of 100,000 (British pounds) at 6% with
monthly payments. How is the monthly payment amount computed? How is
the monthly interest amount computed in an amortization schedule?

I must've caught UK people at work. In the meantime ....

One online source [1] computes the monthly payment by PMT(6%, 180,
-100000)/12, which is about 858.02 (must be rounded). That agrees
with an independent online UK mortgage calculator [2].

But another online UK mortgage calculator [3] calculates the monthly
payment in a manner that I am accustomed to, namely PMT(6%/12, 180,
-100000), which is about 843.86.

Is one method more prevalent than the other in the UK?

Based on that, I might think that the monthly interest rate is
RATE(180, 858.02, -100000), which is about 0.521746%.

On second thought, the first payment formula suggests to me that
interest should be computed on annual basis, namely 6% of the
outstanding balance at the beginning of the year. I would expect the
annual interest to be prorated to each payment in some fashion.

The obvious method would be to divide the annual interest equally.
But lenders tend to like formulas that capture interest as early as
possible. I suppose any rule is possible -- for example, one based on
the Rule of 78 over 12 months.

Is there a conventional method of prorating the annual interest for
the first method of computing the payment amount, namely PMT(6%,...)/
12?

Second, in another thread, the OP says that UK mortgage interest is
"calculated daily and added monthly", and that the daily interest is
compounded. Is that correct?

If that is correct, how is the daily rate computed?

I think this question is valid even if the second payment formula
applies. I am not sure how that would be done even in the US, if the
monthly payment is computed by PMT(6%/12,...).

-----
Endnotes
[1] "Mortgage repayment tables" link on
http://www.cml.org.uk/cml/consumers/calculator
[2] http://www.bbc.co.uk/homes/property/mortgagecalculator.shtml

[3] http://www.mortgages.co.uk/calculator/mortgage_calculator.html