Key Post A guide to mortgage repayment calculations

Brendan Burgess

Founder
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38,902
As always, comments, corrections and suggestions for layout very welcome - Brendan

There have been a few questions on askaboutmoney which have been very difficult to answer without explaining the background to mortgage calculations. For example:
Bank of Scotland offer to write off my arrears. What is the catch? People often confuse interest payments with the full repayment. The purpose of this long thread is to explain the background to how mortgage repayments are calculated in a systematic way.

Subjects covered:


Not covered

  • Applying for mortgages
  • tax relief
  • investment mortgages
  • the fairness of interest rates

The standard repayment or annuity mortgage

Let’s start with a simple example of a €100,000 mortgage at 4% for 20 years.

You can get the repayments from Karl Jeacle’s excellent Mortgage Calculator

Code:
             interest           capital           balance
  2001      €3,939.34         €3,332.42         €96,667.58
  2002      €3,803.58         €3,468.18         €93,199.40
  2003      €3,662.27         €3,609.49         €89,589.91
  2004      €3,515.21         €3,756.55         €85,833.36
  2005      €3,362.17         €3,909.59         €81,923.77
  2006      €3,202.90         €4,068.86         €77,854.91
  2007      €3,037.11         €4,234.65         €73,620.26
  2008      €2,864.59         €4,407.17         €69,213.09
  2009      €2,685.04         €4,586.72         €64,626.37
  2010      €2,498.17         €4,773.59         €59,852.78
  2011      €2,303.67         €4,968.09         €54,884.69
  2012      €2,101.28         €5,170.48         €49,714.21
  2013      €1,890.64         €5,381.12         €44,333.09
  2014      €1,671.40         €5,600.36         €38,732.73
  2015      €1,443.21         €5,828.55         €32,904.18
  2016      €1,205.76         €6,066.00         €26,838.18
  2017      €958.61           €6,313.15         €20,525.03
  2018      €701.41           €6,570.35         €13,954.68
  2019      €433.73           €6,838.03         €7,116.65
  2020      €155.12           €7,116.64         €0.00
The repayment is calculated so that the mortgage is repaid over 20 years

Assuming that the interest rate stays the same, the repayment stays the same for the whole 20 years ie. €605.98 per month which is €7271.76 per year.

Each repayment contains an interest and a capital element
This is a really key concept and is worth dwelling on. The annual cost of a mortgage is the interest you pay on that mortgage. So in year 1 above, the cost of borrowing that money is €3,939.

The capital repayment is a form of saving. The €3,332.42 in capital repaid during the year has reduced your outstanding mortgage to €96,667.

A lot of people say “My mortgage costs me €605 per month”. This is not the same as a tenant who says “my rent is €605 per month”. The rent is the true cost of living in the house. For the home owner, the true cost of the mortgage is the interest element. In the first year above, roughly half the repayment is interest, so the true cost of the mortgage is around €330 per month. By contrast, in 2020, the true cost of the mortgage is only €13 per month in interest.

This is a very important distinction to make. Many people who are struggling with their finances and running up overdrafts and credit card bills are, at the same time, paying capital off their mortgage. So they can be borrowing at Credit Card rates of 16% to pay off a loan which is costing them 4%. This makes no sense if they can get their lender to agree to reduce the capital element of the repayment.

Checking that you have been charged the correct interest.
It is very easy to get a rough idea of how much the interest should be on your mortgage. At the early stages, you are not repaying much capital, so the balance at the end of the year will be just a bit below the balance at the start of the year. So in Year 1, the balance is €100,000. The interest rate is 4%, so the interest charged should be around €4,000.

It gets a little bit more difficult in later years. Take 2017 for example. At the beginning of the year, you owed €26,838 and at the end you owed €20,525, so the average balance during the year was about €24,000. 4% of this would be €960.

You can also use this Excel spreadsheet to calculate the interest in a more exact way.

What happens when interest rates change?

At the start of year 11 above,
balance remaining|€60,000
Interest rate|4%
Remaining term|10 years
Monthly repayment|€605
If the interest rate increases to 5%, the repayment increases by around €30 per month to €637. However, in the first year, when you owe €60,000, the interest element of the loan has increased by 1% of €60,000 or €600 a year or €50 per month. When the interest rate increases, more of your repayment goes to paying the interest, and less to paying off the capital.

Play around with the Simple Mortgage Calculator to see the effect of interest rate changes on your repayments.
 

Brendan Burgess

Founder
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38,902
What happens if I increase my monthly repayments or make a capital repayment?

If you increase your monthly repayments, you will pay off more capital with each repayment. As a result, your loan will be repaid quicker.

At the start of year 11 above,
balance remaining|€60,000
Interest rate|4%
Remaining term|10 years
Monthly repayment|€605
What happens if you increase the repayment to €800 per month?

Using the Simple Mortgage Calculator put in the above data on line 1: remaining amount; remaining term and interest rate.

Click on the green arrow and it will replicate this line a few times. You can work backwards by changing the term of the loan. So on line 2, change the term to 8 years and you will see that the repayment required to reduce it to 8 years is only €729. On line 3 change it to 7 years, and you will see that an increase to €818 will pay off the loan in 7 years. So paying €800 per month will reduce the remaining term to just over 7 years.

What happens if I pay off a once-off lump sum?
At the start of year 11, you owe €59,852 – say €60,000 for simplicity. You will pay this off over the remaining 10 years at €605.98 per month.

If you pay off €20,000, you will owe €40,000. You can choose to pay this off over the remaining 10 years or over a shorter time period if you prefer.

From the simple loan calculator, you will see that your monthly repayment will drop to €405 per month if you choose to pay it off over ten years.

If you keep up your monthly repayment, and you will have the loan paid off in 6 years and 3 months.

Which is better? This depends on your financial priorities. For example, if you have not funded your pension properly, you may prefer to increase your contributions to your pension fund rather than pay off your mortgage. (But then you might have been better to use your lump-sum to increase your contributions to your pension scheme)
Should I use a lump-sum to reduce my mortgage?
 

Brendan Burgess

Founder
Messages
38,902
What happens if I can’t afford to keep up my full repayments?

The lender could offer you one of the following arrangements
Extend the term of the mortgage
Reduce the repayments temporarily, but increase them when you can afford higher repayments

At the start of year 11 above,
balance remaining|€60,000
Interest rate|4%
Remaining term|10 years
Monthly repayment|€605
Extending the term of the mortgage

Using the Simple Mortgage Calculator put in the above data on line 1: remaining amount; remaining term and interest rate.

Your monthly repayment is comprised of €200 interest and €400 capital. If the lender agrees to extend your loan to, say 15, years, the monthly repayment will drop to €443.

Reduce the repayments temporarily, but increase them when you can afford higher repayments.
The lender may offer you a full payment moratorium for one year, but then insist that you pay off the loan over the remaining period of 9 years so that it is paid off by the original end date.

At the end of the year, the amount outstanding will increase by 4% or €2,400 to €62,400.

To pay off €62,400 over 9 years, the Simple Mortgage Calculator shows you that this will increase your repayments to €689 per month.

Of course, the lender may offer you both. They could offer you a moratorium on payments and also extend the term of the loan.
 

Brendan Burgess

Founder
Messages
38,902
Arrears

Arrears is the total of the “payments due but not made”. It includes interest and capital.

The balance due on your mortgage is
Opening balance
+ interest charged
- repayments
= closing balance

At the start of year 11 above,
balance remaining|€60,000
Interest rate|4%
Remaining term|10 years
Monthly repayment|€605
If you miss a few payments, your account will look like this:

|January|February|March|April|May|June
Interest charged|€200|€200|€200|€200|€200|€200
Mortgage balance at end of month|€60,200|€60,400|€60,600|€60,800|€61,000|€61,200
Arrears|€605|€1,210|€1,815|€2,420|€3,025|€3,630
These figures have been simplified. The €200 increases each month as the interest charge is higher on the increasing balance.

It’s very important to distinguish between the arrears balance and the mortgage balance. The arrears balance is just a note of the amount due but unpaid. The true amount still outstanding on your mortgage is the Mortgage Balance line above.

Options for dealing with arrears


Pay off your arrears in one lump-sum and revert to your normal monthly payments of €605
If you miss the payment at the end of January but you pay it off within a few weeks, you will be back on track and you continue making your normal payments of €605 per month.

Write off the arrears and pay increased monthly payments over the remaining period
Let’s say you lose your job in the above example, but you get a new job in July and you are able to service your mortgage again, but you are not able to pay the arrears.

The bank may agree to write off the arrears – this is also known as “capitalizing the arrears”. This does not save you anything and it does not cost you anything. At the end of June, you will still owe €61,200.

The bank will increase the monthly repayment to €646 per month and this is sufficient to pay off your loan within the original timeframe.

Write off the arrears and extend the mortgage
The bank may agree to write off the arrears and leave your monthly repayment at the original €605. This will add a bit more than 6 months to the time left on your mortgage.

Leave the arrears in place but just not chase them
As a matter of policy, some lenders don’t like writing off arrears. They will leave them in place, but not chase them. If you subsequently fall behind and they need to take legal action, they are in a stronger position because you have arrears.

Increase your repayments temporarily to pay off the arrears and then revert to your normal monthly payment
The lender might ask you to increase your repayments to €1,200 per month for the next 6 or 7 months to clear the arrears quicker.
 

dewdrop

Frequent Poster
Messages
1,299
I agree many people find it difficult to grasp the repayment situation. In my experience what causes confusion is that when it is explained that the repayment in effect goes towards meeting the interest and providing a capital reduction a person will say am i not paying interest twice as it is also charged up to the Mortgage loan account. Sometimes i found it is easier just to say how much do i need to lodge to ensure the loan plus interest will be cleared off over the given period.
 

Brendan Burgess

Founder
Messages
38,902
I agree many people find it difficult to grasp the repayment situation. In my experience what causes confusion is that when it is explained that the repayment in effect goes towards meeting the interest and providing a capital reduction a person will say am i not paying interest twice as it is also charged up to the Mortgage loan account. Sometimes i found it is easier just to say how much do i need to lodge to ensure the loan plus interest will be cleared off over the given period.
Hi dewdrop

That is very interesting. I have seen that confusion and never really got it. I might try to reproduce a mortgage statement to show what it looks like.

Brendan
 

LDFerguson

Frequent Poster
Messages
4,094
Hi Brendan,

Excellent summaries.

Leave the arrears in place but just not chase them
As a matter of policy, some lenders don’t like writing off arrears. They will leave them in place, but not chase them. If you subsequently fall behind and they need to take legal action, they are in a stronger position because you have arrears.
It might be relevant here that the Irish Credit Bureau records arrears for five years after the arrears have been cleared. So clearing the arrears (if that's an option for you) can mean your Credit Bureau report is improved earlier than leaving the arrears in place.

On dewdrop's point, most lenders calculate interest daily. It varies between lenders how often they actually add the interest to the account. Monthly is popular.

So in your example of €100,000 owing at 4%, the daily interest is €100,000 x 4% / 365 = €10.96. A lender will add €10.96 x 30 to your account at the end of a 30-day month. This will be added to the loan balance, but your monthly repayment will be deducted. As long as your monthly repayment is greater than €328.80 (30 x €10.96) the effect will be that your balance will reduce. From the next month, the daily interest will be calculated on the lower balance and so on.
 

leonmahon

Frequent Poster
Messages
178
Very interesting reading here. I'm new to all this and am learning a lot.

On overpaying, or paying a lump sum, do I understand this correctly: In effect, any amount paid over and above the normal monthly payment (capital+interest) will go wholly towards reducing the remaining capital amount?
 

Brendan Burgess

Founder
Messages
38,902
Very interesting reading here. I'm new to all this and am learning a lot.

On overpaying, or paying a lump sum, do I understand this correctly: In effect, any amount paid over and above the normal monthly payment (capital+interest) will go wholly towards reducing the remaining capital amount?
I learned a lot writing it!

Yes, you are correct. At any time, there is a balance outstanding on your mortgage. If you make a payment, the balance is reduced.
 

leonmahon

Frequent Poster
Messages
178
Apologies but one more question. If mortgages are set so that the interest is divided along the entire term, and we begin overpaying, will we just end up paying the same amount of total interest but just over a shorter period of time?

EG we were considering getting a 30 year mortgage but trying to overpay so that we'll pay less interest overall (while protecting us should interest rates go through the roof). But if we paid the 30 year mortgage in 25 years, would we end up paying the same amount of interest as if we had taken out a 25 year mortgage in the first place?
 

Brendan Burgess

Founder
Messages
38,902
No.

Interest is calculated every day on the balance outstanding. So if the rate is 5% and you owe 100,000 this morning, you will owe 100,000 + one day's interest which is €13.70, this evening. Tomorrow you will be charged one day's interest on €100,013.70.

If you increase your repayments or if you pay off capital, you will pay less interest.

Brendan
 

Mrs Vimes

Frequent Poster
Messages
905
But if we paid the 30 year mortgage in 25 years, would we end up paying the same amount of interest as if we had taken out a 25 year mortgage in the first place?
Yes, that is correct, but as you imply, if things get too tight for you, you could slow down the overpayments for a while and hope to catch up later. If you took out a 25 year mortgage in the first place the bank may not agree to allow you to lengthen it.
 

dewdrop

Frequent Poster
Messages
1,299
Another point which i think often confuses people is the question of interest. I think it is important to stress that while it is calculated on a daily basis on the balance outstanding the interest accrues (i.e. not added to the loan) due but is not charged/added to the loan until the charging date which now is every quarter. In the past it was half yearly. Maybe i could have put this point across in a better fashion.
 
J

JoeB

Guest
A point I find nice to explain is that if you currently pay 1,000... which is 700 interest say, and 300 capital. .. then by increasing your repayments by only 30%, to 1,300, you can double your capital payments.. and thus save interest and time. So overpaying should be stressed as valuable, and something to be done when times are good (rather than upgrading the car for example)

The maths around mortgage payments, with extensive work done on the effect of overpaying, and saving deposits, and other scenarios, should be on the school curriculum, as opposed to some maths about integrating the area under curves say. This seems very obvious to me,.. the schooll curriculum should focus on areas of knowledge that adults currently lack, and could use.



It doesn't matter how frequently interest is calculated, if is only actually applied to the account less frequently. If applied less frequently then it can be correctly considered to be calculated at that lower frequency.
In other words, if calculated daily, but not compounded daily, then the total of the daily calculations give the same answer as a longer period calculation.

(There is the practical issue of there being different numbers of days in each month, and also mid month payments, so a daily rate must be used in reality.)
 
B

bocoip

Guest
Really informative thread.

I took out a mortgage last year and when reviewing my end of year statement and comparing it with the amortization tools mentioned above, it looks like I was over charged in the amount of interest paid (by over a grand).

My question is, what my best approach to getting this resolved?
 

boe

Frequent Poster
Messages
103
Moved from this threadLump sum Mortgage towards capital or interest? - Brendan

Reducing the monthly payments without changing the term will generally be better. You are free to keep up the higher payments and end the mortgage sooner, but if you need to you can drop to the lower payments easily enough.
I've read the Key Post and have a follow-on question on this. If I want to pay a lump sum off my mortgage, the advice seems to be to leave the term the same and reduce the payments. Will you save the same amount in interest by doing this as you would if you just chose to reduce the term?

If say, I paid the lump sum, kept the term the same and then just continued with the old repayment amount (overpaying), what effect would this have? Would I save even more on interest and end up finishing the term earlier?

Thanks
 

Brendan Burgess

Founder
Messages
38,902
Interest is charged on a daily basis on the amount of the mortgage outstanding.

If you have €100,000 left with a 20 year term @4.5% , the repayments will be €632 per month. .

If you reduce the term to 12 years, the repayment will be €900 per month.

If you leave the term at 20 years, but pay €900 per month anyway, the effect is exactly the same. However, if at some later stage, you need to reduce the repayments to €632 per month, you can do so.

So the key is to get as long a term as possible , even if you want to pay it off as quickly as possible.
 

boe

Frequent Poster
Messages
103
Thanks Brendan, that makes sense. I was trying our various scenario's using Karl Jeacle's calculator and it wasn't correlating.
 

Roses&Guns

Registered User
Messages
1
Good Afternoon,
I have been trying to fathom the Arrears concept and its implications for Debt (Capital) repayment. My Logic (as someone who worked in retail Banking) and indeed my understanding has been tested by this thread!
I seem to recall arrears being capitalised onto the mortgage, this had the effect of increasing the Capital Balance by the amount of the Arrears !! I am 90% certain that this was the case ( I am a few years out of retail Banking).
I would currently argue that the portion of Arrears that effects the repayment term or amount should only be the interest portion- indeed the interest portion of the missed payment.
I drove to work this morning trying to rationalise this concept.. given I have spent many years in Banking I am almost disappointed in myself that I had not challenged the concept in a detailed manner up until now.
So My query really only further confuses the issue- If you have missed 10 payments of €1500 (monthly repayment) - say €100,000 MortgageLoan- of which 1000 is capital and 500 is interest- thereby creating an arrears balance of €15000 . Loan outstanding at start of year was €100,000-
is the total debt now €115000 or €105,000?
I would expect the Bank to be paid its missed interest of €5000!
But I would not expect the Bank to be paid Twice for the Capital portion (ie €10,000)

However If arrears are capitalised in the manner I recall above- it would seem that the total debt due would indeed be €115,000.00

Is there a legal stance or indeed a regulatory stance on same?
Roses&Guns
 
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