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I struggle to understand how mortgage and interest rates works. (I made up the figures to keep it simple)

Some facts:

  • My balance is £206.000
  • Each month I repay £950 (capital + interest)
  • I do a monthly early repayment of £1000
  • My interest rate is 3.23% per year

So each month, I pay £1950 into that pot.

First of all, my online statements keeps saying that the term of the mortgage is 29years and few months, this goes down a month each month even if I double the amount I repay. If I repay for that amount of time (and even the 950 minimum) surely I'll end up paying more that I should !?

My current understanding of things is that the £1000 are directly subtracted from the balance, and the 950 are a bit harder as some of it is subtracted and some just goes into the banks's pocket (how much would be useful to know)

My main question is : What is the formula to calculate the cost of skipping a £1000 payment on a given month ?

  • Interest is calculated daily, using a day interest rate and compounded. The prepayment is deducted from the principal the day you pay it/or the bank receives it. So get an excel sheet, punch in all data and calculate. – DumbCoder Oct 12 '16 at 14:55
  • This is UK, right? Do you have any early payment/prepayment penalties/costs/fees? Are you actually paying direct to principal, or are you "pre-paying" the next month's payment? – Joe Oct 12 '16 at 15:32
  • @Joe it is in the uk, I don't have any penalty under 10% of remaining balance each year, and I'm doing everything to be under that threshold. – 0x1gene Oct 12 '16 at 15:35
  • Using bankrate.com/calculators/mortgages/amortization-calculator.aspx you can test how a payment against the principal is going to affect your mortgage length and total interest paid. You will see that paying against the principle early in the mortgage is more beneficial than paying it in the middle or towards the end. For example, I applied a $5,000 principal payment for January 2017 and the payoff date became August 2045. Applying $5,000 in January 2027 pushed the payoff date to December 2045. You can expect a similar yet more subtle effect with $1,000. – MonkeyZeus Oct 13 '16 at 19:35
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You refer to your monthly "online statements". Does these have an entry for "outstanding balance" or something similar. Does it go down by slightly more than 1000 each month when you make both a regular and extra payment?

In response to your main question:

Look at it this way:

You owe a certain amount of money at the start of the month. It grows at the stated interest rate throughout the month, reaching a new balance owed by the end of the month.

Then you throw some money in, reducing the balance owed, and the whole process continues, month by month.

If you throw in more each month than that months growth, then eventually you'll pay off the whole thing.

The regular payment (950 in your case) is designed to pay off all the month's growth and some of the previous balance, thereby bringing the balance owed to zero in the 29+ years you mentioned. Paying more than that amount will decrease the balance owed, and thus the growth for the next month, shortening the time to pay off the total,

If you skip a 1000 extra payment, you'll need to pay a months mortgage interest on the larger balance owed, so the actual "cost" is the month's interest on 1000, or about 2.70

EDIT: This assumes that the extra payment is truly only "delayed", and that the next month the regular 950 payment, the delayed 1000 and that month's usual 1000 are all paid. If you continue to postpone the extra 1000 payment, the costs will skyrocket as others have shown...

The danger is that the mortgage company is regarding the extra payments as an early payment and is just holding them (at no interest to you)to make the regular monthly payments on schedule. You really need to be sure that the reduction in balance owed each month reflects the extra payment.

  • The cost is rather more than "one months' interest" on that amount. You're adding an extra $1000 to every month. For 29 years. – Joe Oct 12 '16 at 19:08
  • The question refers to delaying the extra payment, rather than eliminating it. Am I being too picky? – DJohnM Oct 12 '16 at 21:15
  • Well, delaying an extra payment one month is identical to eliminating it, in my book, if you're otherwise making one every month (except perhaps you pay a bit more the last month, or you pay one extra payment)? Unless he's considering making a 2000 pound extra payment the next month, but that doesn't seem the case? – Joe Oct 12 '16 at 21:17
  • Answer edited... – DJohnM Oct 12 '16 at 21:25
  • Like @Joe said is more deleting the payement as I don't plan to pay 2K the next month. Question edited – 0x1gene Oct 13 '16 at 9:38
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First of all, my online statements keeps saying that the term of the mortgage is 29years and few months, this goes down a month each month even if I double the amount I repay. If I repay for that amount of time (and even the 950 minimum) surely I'll end up paying more that I should !?

The online statements that show the next payments and balances; most banks don't revise this. This is a static statement generated once in 2 years and keeps getting shown notionally as if you are making normal payments. So don't pay to much attention to this. You are right that the number of years should decrease faster.

You would get a yearly statements, just make sure all your payments are reflected in it.

My current understanding of things is that the £1000 are directly subtracted from the balance, and the 950 are a bit harder as some of it is subtracted and some just goes into the banks's pocket (how much would be useful to know)

You could do this in Excel.
Opening Balance: Initial Amount
Interest: = (Opening Balance*Interest Rate*30[or 31 or 28])/365 [or 366]
EMI: 950
Additional Payment: 1000
Principal Paid: EMI - Interest
Closing Balance: Opening Balance - Principal Paid - Additional Payment

On the next row, this Closing Balance will be your Opening Balance

Run this for your years and you should be able to see how the interest reduces over period.

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It's quite easy to see the difference, without any formulas; though if you want to see the formula, google 'mortgage payment calculator' and you'll find it laid out well. Here's the approximate formula:

(Payment) = (Principal) * (Rate) * (1+Rate)^(Number of payments) /
                                 ((1+Rate)^(Number of payments)-1)

And then of course total cost-of-borrowing is Payment*(Number of payments). Remember to calculate rate as a monthly rate (look at your documents; .0323 might be your annualized compounded rate, or it might be 12*monthly rate, depends on how your local rules are). Assuming .0323 is 12*monthly rate, as it would often be in the US, then:

M = (206000)*(.0323)*(1.0323)^360 /
                     (1.0323^360-1)

M = 895, so 950 is a bit above that - either implying the rate is higher by a bit than you say, or there are some fees (maybe taxes?) or something else in there.

Then, at any point, you can determine the "cost" of not paying an extra 1000 pounds off by entering the details in there - make sure to fix the right number of payments remaining.

Then look at the difference. The difference in the "total amount owed", minus 1000 pounds, is the amount it would cost you to skip one extra payment. That's because what you're effectively doing is, right now, reducing the total principal.

Of course, if you're skipping that payment somewhere down the line, the cost will be less - as there's less time for that amount to generate interest - but it should give you an idea.

You can also determine an approximate answer by looking at your mortgage closing documents. Assuming the UK works roughly like the US, one thing your lender ought to tell you (in writing) is the total cost of borrowing. I.E., what the total amount of money you'll pay after 30 years. Since you may not have a fixed-rate mortgage like we do in the US, it may be approximate, but the concept should still be there.

In your case, you're going to pay a bit over 320k pounds over 30 years at that interest rate. (A bargain!) Divide 320k by 206k, and you get a ratio of 1.56. Each pound you borrow costs 1.56 pounds over the life of the loan - so reducing that amount by 1000 pounds would reduce your total cost for the life of the loan by 1560 or so (1562.80 by my reckoning).

Now, every additional 1000 pounds you pay off reduces your cost by a bit less than the first one (the first one is 1000 pounds you'd have had for 30 years, but the second one is 1000 pounds for 29.8 or so years, the third by 29.5 years or so, etc.); there's a diminishing return. But you can always recalculate the "if I had started the mortgage now" amount, and calculate it with/without the extra 1000 pounds, and know the difference of that particular skipped payment.

For example, let's say you pay 1895 per month (I am assuming my model here, assuming the extra 55 are going to taxes or something non-mortgage related), and two years in want to skip a payment. Plugging things in, each payment of 1000 pounds is saving 520 extra pounds over the life of the mortage (rather than 560 pounds as at day 1). You'll see the amount stay more or less stable for 10 years or so, then start to drop more quickly as the principal starts dropping more rapidly after around ten years (since its not linear, but exponential).


All of this assumes that you're accurately describing how the 1000 pounds is applied - to the principal. Not all localities automatically do that; I'm not in the UK so I don't know their law, but it used to be common in many places that "Extra" payments were assumed to be making an early payment of the next month, and so wouldn't be applied until then - not saving you any interest. That's slowly going away as more places realize that's very consumer unfriendly, even though it sounds "nice", so hopefully it is not true in your case: but verify with your lender that what you think should be happening with the money is.

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Some mortgages don't allow overpayments, and your extra 1000 would simply be applied to future due monthly payments. If this is the case, you would be now 'months ahead' in paying, but didn't save a single penny on interest.

This form of mortgage is the standard in Germany, and mostly unknown in the US (most people in the US find the concept even outrageous). I don't know which form is possible/used in the UK, but you need to verify this for your loan.

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I think a simple amortization table would help you. The above answers (in my opinion) don't show you a direct correlation between the affect of payment and interest on it's reduction of the balance (or principle).

I changed the symbols to pounds. i.e - I'm from the U.S. and am treating the problem as such.

This shows the numbers inside an amortization chart:

and here are the formulas:

The first image calculates your payments (naturally you're actually paying more for the sake of convenience) and subtracts the interest. The "principal" that is left is the reduction to the balance. Your assumption that a prepayment of 1,000 is a direct reduction to the balance is correct. Note, as you continue to pay, the interest amount is reduced perpetually reducing the balance more quickly in later years.

If you follow the formulas and replicate this in an Excel sheet, you can find how long it will take you to repay the loan. Make sure to correct the amount and years as mine were an estimate of the original figure.

If there is anything I am leaving out, or would like me to explain, feel free to comment.

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