How would I work out what the optimum payment would be to fix a standing
order for an overpayment on a mortgage over 3 years when the maximum allowed
is 20% of the outstanding balance per year (daily interest at a fixed rate
of 4.99%)?! Mortgage amount is 45k.
Thanks for any help!

Does "mortgage over 3 years" mean that (without the overpayments)
the loan is expected to be paid off in 3 years, or does it mean
it's longer-term than that, but for the first 3 years there is a
ceiling on annual overpayments, which you want to exploit to the full?
Why do you want to make a standing order for the whole 36 months?
Why not just note that in year 1 you may overpay by 20% of £45k,
which is £9k, and thus make the monthly overpayments a twelfth
of that (£750)?
Then, of course, you would need to amend the standing order downwards
prior to month 13 and month 25, to take into account the new reduced
balances of which you may overpay 20% in years 2 and 3.
On the other hand, the rules of your scheme may be more subtle.
Instead of meaning that *in addition* to your normal payments you may
make overpayments during the course of the year which total no more than
20% of the year's opening balance, it could instead mean that, based on
your normal payments, there will be pre-determined end-of-year balance,
and you must not make more overpayments than would cause the end of year
balance to drop below 80% of that predetermined value. The calculation
would be a little more interesting then, but not difficult. Need to know
term length, by the way, in order to predetermine the end of year balance.

I knew I'd forgotten something! Its a 5 year term, 3 year fixed. I want to
pay it off in 3 years by overpaying, but there's this 20% max overpayment by
year clause that can only be paid in standing orders, so I just wanted to
work out the optimum to overpay each month so I don't have to remember to
re-adjust every year to the new 20% / 12 months value per month overpayment.
Hmm, I suppose you have got a point there - those two maximums are
different, but I wonder by how much? I'll have to investigate the specific
wording when I get a chance.
Thanks for the help.

I think you should make the effort to remember. With as short a term
as 5 years, the balance 24 months in is going to be very much smaller
than at the start, and therefore so will 20% of it. You'd be wasting
a fair bit of repayment opportunity during the 2nd, and especially
during the first, year.
On the other hand, let's run the calculation backwards and ask what your
payments would have to be to shorten the term from 60 to 36 months. To
repay £45k over 60 months at 4.99%/12 per month would involve monthly
payments of £849. To repay over 36 months instead would cost about £1349
a month, which is a £500 overpayment per month, 12 times which is £6k,
so that's well below the £9k (20% of £45k) limit.
But you're wasting 1/3 of your opportunity.
Now, in that scheme, the balance after year 1 would be down by a factor
of (1-1.0499^-2)/(1-1.0499^-3) which is 0.68276, i.e. £30724, bringing
your overpayment limit for year 2 to £6144, or £512 a month. So it
would still be OK to keep the overpayments payments at £500.
But after year 2 the factor is (1-1.0499^-1)/(1-1.0499^-3) which is
0.34969, making the balance £15736, and the overpayment limit £3147
or £262 a month, so you're scuppered. Your objective of clearing the
loan in 3 years using a 36-month-fixed SO is unachievable.
What, according to the rules, happens when your overpayments are too
high? If they bring it to your attention, it won't matter if you've
forgotten.

I know, I'm experimenting in methodologies at the moment and soon realised
that. Its a shame there's no tools to work this stuff out easily. The best
I'd found was

formatting link

- which is very useful, but not quite what I need...
Thanks very much for your calculations - that has given me more to think
about. I have now emailed the nice lady at the mortgage company to see if
she can come up with the best solution for me.
A 5% penalty. Ouch.

Out of interest - is it possible then to finish paying the mortgage off in 3
years by overpaying the full 20% on a flexible basis? ie, 750pm 1st year,
512pm, 2nd year and 262pm in the last year - does that work out to a 0
balance after 3 years? I just don't know where to begin to work these things
out!

The above is wrong, by the way, Tim must be slacking not to have picked
up on this. The factor should be (1-f^-12)/(1-f^-36) where f=1+0.0499/12,
and I had short-handed f^-12 and f^-36 to F^-1 and F^-3 but written F as
1.0499 instead of the f^12=1.051057 it ought to have been. Head duly hung
in shame for three whole seconds.
You need to be careful. The £512 figure for year 2 was based on overpaying
£500pm in year 1, so if you actually overpay £750 in year 1, the year 2(3)
limit will be a bit lower than £512(£262).
But the answer is yes, almost.
The monthly payments are P = An * r / (1 - f^-n) [1]
Where An means "amount owing when there are still n months to go),
and r is the monthly interest rate (in this case 0.0499/12),
and f=1+r.
To work out the balance after 12 months, you solve [1] for An
and plug in k instead of n, using k=n-12 (i.e. you work out the amount
owing when there are 12 fewer months to go than there were originally.
Ak = P*(1-f^-k)/r [2]
and if you substitute the expression above for P, the 'r's cancel out
and you get
Ak = An * (1-f^-k)/(1-f^-n) [3]
One more thing. To answer the question "if I start with A, and pay P per
month, what will the balance be in 12 months' time?" you first need to
work out how long it would take to pay off.
To do this, solve equation [1] for n:
(1-f^-n) = A * r/P
f^-n = 1 - A*r/P
log (f^-n) = log(1-A*r/P)
-n = log(1-Ar/P)/log(f) [4]
Then, and only then, can you use this n (and k=n-12) to work out a
new balance using [2] or [3].
This is what I did earlier:
First use [1] to work out P for n`, which is £849.
Then overpay the max £750, and this gives a new P of £1599,
and if starting from £45k, [4] gives a new n of 30. Then
use [3] to work out the end-of-year-1 balance, using n0 and k.
That's £27669 which leads to a max monthly overpayment for year 2
of £461.
So, next step: P = £849+£461 = £1310. Use this and £27669 in [4]
to get a new n of 22.15, so use a k of 10.15 to work out the year 2
end balance using [3]: I get a new balance of £12995 leading to max
overpayments of £216 per month.
New P for year 3: £216+£849 = £1065.
New n: 12.55
So there you go. Target *almost* reached, and the loan will be paid
off about halfway through month 37.
You need to redo everything each time the interest rate changes,
but if you're on a fixed rate, you'll be laughing.

Well, I dunno if that made you look like an absolute fecking genius, or me
an absolute numbnuts, but as long as your calculations are correct (and I'm
partially willing to stake my mortgage on it by sending off the forms
tomorrow morning!), then whaddaya reckon I'll might need to save up for a
lump sum to pay on the first day after the fixed rate has finished (ie the
balance?). I'm too thick to even work that one out!
I'm asking this because this is the crux of whether I chose one mortgage
over another. The other option is a fixed 3 year deal for 5 years at 5.38%
with 500 fees (the 4.99% deal = no fees). But the 5.38% deal lets me pay
off max of 500pm every month and all this time I've been trying to work out
which option will cost me less when I've (hopefully) paid the mortgage in
full in 3 years.
So far as I can follow, I'd be saving 1552.35 on the 4.99% deal if I pay
750 / 461 / 216pm in years 1/2/3 as you suggested (total over payment of
17124 vs 18000 on the 5.38% deal) - ie:
36 * 857.06 then 500pm overpayment + 500 fees = total payments of 49240.35
vs.
36 * 849.00 then 750 / 461 / 216 in years 1/2/3 overpayment and no fees 47688
= difference of 1552.35
Hope this is correct?! But then what was that you said about paying it off
halfway through month 37 - how much?!!!

No need to save up, it would just be a partial normal monthly payment for
the 37th month.
Well, it ought to be obvious that a 4.99% deal is better than a 5.38% deal
even if the latter did not involve a £500 fee. Also as the latter limits
the overpayments to £500, while the former allows them to go to £750 at
least in the first year (it's better to repay as much as you can as early
as you can, because overpayments in a way "earn" interest as though they
were in a savings account paying untaxed interest at the mortgage loan
rate).
What I meant was that at the monthly amount to which you switch at the
boundary between year 2 and year 3, it would take 12.55 months to pay off.
In other words, you should expect to make a 37th payment which would be
a bit more than half of the 36th.
I guess that makes the difference just under £1k, so still worth it.

A-ha! I see, I see, been thinking about it all too much that its tied my
brain a little.
Or should that be tied my little brain?!
A big thanks for your help - most appreciated.

[]
Hassle them to find out the *exact* rules, including when they calculate
interest - I once persuaded a bank that paying 3-months mortgage in
advance (they calculated interest on the average monthly balance and
applied it quarterly) on /just/ the right date each quarter *did not*
count as an overpayment.
rgds, Alan

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