# Prepay interest



## Fiddlybits (17 Sep 2018)

Is it possible to prepay interest in the credit union? I prepaid my loan and am at correct point on amortization table but missed a few weeks and got a letter saying I am in arrears. I queried this and was told it is interest outstanding.


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## WizardDr (17 Sep 2018)

Interest in CU is accrued on a daily basis.
The first thing is when the payments were made the systems look at accrued interest first and reduce that to NIL
then reduces your principal. 
So your interest accrued was zero at that point.
Ask the CU how they treated your payments in advance.


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## Fiddlybits (17 Sep 2018)

*Thanks Wizard. I will contact the CU and check how my prepayments were taken. I thought I would be ok as I was prepaid.*


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## Murky18 (31 Oct 2018)

Fiddlybits said:


> *Thanks Wizard. I will contact the CU and check how my prepayments were taken. I thought I would be ok as I was prepaid.*



how did you get on?  i was in the same position with my loan


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## Fiddlybits (31 Oct 2018)

As Wizard said any accrued interest was taken and though I paid my loan in advance only the principal was reduced. I missed a few weeks around holidays and Christmas and so interest accrued. I’m now back on track and hoping to stay that way!


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## Brendan Burgess (31 Oct 2018)

So, it seems that they are doing the following, which doesn't make much sense to me at least.

This is how it should work in a normal loan where you make the repayments on schedule






Let's say you prepay €2,000 and your monthly repayment is reduced to €400 and miss a few payments





Although you are ahead of schedule, it's seems as if they treat you as being in arrears by the interest charged for months 2,3 & 4.

Brendan


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## Elnino (1 Nov 2018)

Credit unions don't capitalize interest or charge interest on interest so your last table is wrong Brendan. The interest figure per month in months 2 to 4 should be €81 per month. At the end of month 4 the balance owed by the member would be €8,100 principal plus €243 accrued interest. At the end of month 4 the loan would be ahead on principal but in interest arrears.

Normally when someone prepays their loan for a few months the credit union would ask them to make interest payments during their repayment holiday to avoid the situation mentioned above.


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## Brendan Burgess (1 Nov 2018)

Elnino said:


> Credit unions don't capitalize interest or charge interest on interest so your last table is wrong Brendan.



Wow! 

So the Credit Unions don't charge compound interest? They only charge simple interest? 

That is shocking.  Would you have a link to the rules or wherever it says that? 

Brendan


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## Brendan Burgess (1 Nov 2018)

From https://carlowcreditunion.ie/loan-arrears/arrears-faq/

_* Interest is accrued daily based on the loan balance.* When a payment is missed, interest continues to accrue on the loan balance until the next payment is made. Where interest has accrued longer than the agreed repayment term, this is referred to as interest arrears._

The loan balance in ordinary terms is the principal + the interest accrued.  This would suggest that they do charge interest on interest.

But maybe by loan balance, the Credit Union means the principal excluding any interest charged?

It would also explain the fairly artificial statement "your payment is first allocated against interest". 

Brendan


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## Elnino (1 Nov 2018)

When you draw down a loan the credit union's IT system creates an amortization table showing the monthly payments over the life of the loan split between capital and interest. Your first payment is allocated firstly to the interest charge owed for the first month per the amortization table and the remainder to reduce the loan principal. This should be the same way any bank loan works. You will pay more interest at the beginning of the loan and less month on month as the principal falls the same as any other loan.

If you look at a statement for your loan at any point in time it will have 3 main balance figures at the end
1. The principal balance - which is the amount borrowed less all payments which have been allocated to principal to date
2. Principal arrears - which can be plus or minus and is the difference between 1 above and what your principal amount owed should be on that date per the amortization table. If you have overpaid the loan you will have negative arrears which means you are ahead.
3. Interest arrears - if you pay exactly on time as per your repayment schedule this amount will always be nil at the end of the month. If you are in arrears then this will accrue on a daily basis. As already stated you can't prepay interest.

The balance you owe the credit union at any time is 1 + 3. 

Hopefully this explains the way interest is calculated by credit unions and it is actually fairer than the way most banks do it as if you overpay your credit union loan you will be charged less interest over the life of the loan and you will clear it quicker. Obviously if you go into arrears then you will be charged more interest over the life of the loan.


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## Brendan Burgess (1 Nov 2018)

Elnino said:


> This should be the same way any bank loan works.



No mainstream bank works the way you suggest. 

They all charge compound interest. 

In other words, they add interest to the principal and charge interest on the full balance. If you don't meet your loan repayments on time, you get charged interest on the total.

The credit union may well charge simple interest. I am surprised, but I suppose it's possible.  But no other lender does.

Brendan


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## WizardDr (2 Nov 2018)

First the CUs calculate daily interest on outstanding principal balance the same as every financial institution does. 

Second it does not 'apply' the interest to the principal balance unlike most financial institutions.

Third each payment you make is firstly applied against accrued interest and the balance against principal.

So if you took out a 12 month loan of €1,000 on 1/January and agreed to 12 monthly payments at end of month approx:
- you would pay €83.33 per month;
- you would clear the loan on last payment
- the APR would be 12.7% (based on €83.33 each month calculating an IRR to find 'r' (say .01 or 1%) and 1.01^12 for those you interested).

If you took the same loan with PTSB at same term, rate, and conditions the payments would be exactly the same.

Because: when PTSB debit the accrued interest on 31 January which is the same date as your payment you are effectively paying the interest and then the principal. You would pay EXACTLY the same.

[The key is when the Banks 'capitalise' or debit the interest. Some are monthly some are quarterly. The quarterly debiting means there is no interest on interest for a quarter.]

If you are late with your payment the interest has been applied and ranks as part of the balance. In the CU case they have not applied the interest and your interest calculation is still on the principal. 

That is the difference.

My view is that the APR implies monthly interest and CUs could in fact abandon the method and debit the interest. It would make NO difference if you pay on time but some of the purists say you cannot charge more than 1% a month but are overlooking that the APR actually assumes a monthly capitalisation and the additional interest is not on the 'payment' (this is being calculated as above) but on the interest that was assumed to be added to the account.


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## Brendan Burgess (2 Nov 2018)

Hi Wizard 

Thanks for that detailed explanation. 

So if I borrow €10,000 from a Credit Union at 12% interest a year and pay nothing at all for 5 years, in the 6th year I will be charged 12% interest on €10,000 and not 12% interest on the mortgage balance of €16,000? 

That is astonishing and I am not sure of the logic behind it. 

Brendan


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## Andrew Murphy (2 Nov 2018)

Brendan Burgess said:


> So if I borrow €10,000 from a Credit Union at 12% interest a year and pay nothing at all for 5 years, in the 6th year I will be charged 12% interest on €10,000 and not 12% interest on the mortgage balance of €16,000?



My reading of the arrears FAQ on Killarney CU would indicate they use the calculation approach as per your example, specifically "When a payment is missed, interest continues to accrue on the loan balance until the next payment is made" i.e. no interest capitalisation. So €10,000 x 0.12 x 5 = €6000 total interest. Quite lenient I'd say!



WizardDr said:


> My view is that the APR implies monthly interest... the APR actually assumes a monthly capitalisation...



Although your view is probably based on the examples quoted, an APR (taken to mean the annualisation of the effective rate, not the consumer credit APR which is a different beast altogether) may be derived from any combination of repayment and interest capitalisation frequency, e.g. weekly, monthly, quarterly etc., and not just monthly. May be I'm just being pedantic


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## WizardDr (5 Nov 2018)

For the avoidance of doubt, the APR is calculated by reference to the payments you have agreed to make and that is an EU Directive. So if for example I quote you 83.33 per month and somebody else quotes 83.33 - the APRs will be same. If a third quotes 85 per month, that APR will be higher than the previous two At the backend as it were, how you derive the payment is irrelevant, what matters solely is the payment.

Technically you are deriving an internal rate of return (IRR) based on the payment profile be it weekly, monthly. Because of the profile, the assumption in the EU model is that capitalisation or payment of interest is made in line with frequency. When you then derive an IRR it is then a rate per period (weekly or monthly). If its monthly then APR: Say r is 1% then (1+r)^12 = 1.12685 which means APR is 12.685% or 12.7% to one place.[If CU quote 'annual rate of 12%' then the daily accrual is 12%/365 etc and for approximately 1% on 12 even months] Note all banks quote the nominal rate like that as an annual rate.

Because of periodic payments you wont 'see' that rate.  However if you do the following test (similar to what Mr Burgess was saying) but make it a one year loan - rate 12% and payments €83.33 - APR 12.7% (or 12.685 if you like)

Draw down €1,000 on 1 January.

Miss all the payments.

Accrue and then add first months interest to original balance at end of January and balance is €1,010.00 - interest €10

Do the same second month and the interest is  €10.10

Repeat for twelve months.

Balance will be €1,120.68

120.68/1000 = 12.68% or 12.7%

This demonstrates how to 'see' the APR.

The point is if the CU does not debit the interest as above it will have €10x12 = 120.00 in interest accrued and 'loses' 68c on a one year loan that misses all of its twelve payments. That said if it had debited interest it would have added 68c to profits it probably wont get back and so its provision would be higher.


Mr Burgess then merely for devilment assumes you miss every payment for 5 years and the conservative nature of CUs is ignored in that they haven't taken in the income in the first place.

Work the same for the 'weekly' payments for a year as homework when you total the interest you will also get whatever the APR is.


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## Andrew Murphy (5 Nov 2018)

The calculation method you outline provides a good approximation of the APR but it is not the way the APR is actually calculated under the consumer credit regulations. Article 19 (Directive 2008/48/EC) states that the APR "shall be calculated in accordance with the mathematical formula set out in Part I of Annex I". The formula is not too dissimilar to that used in solving for an unknown IRR, however it differs in that it handles time periods that are not necessarily of regular interval.

Granted, the formula will return an APR result of 12.7% as per your example, but it is wrong to suggest an APR is derived by computing the IRR and then annualising the periodic interest rate (1% per month in your example) as this is plainly not correct.

I get what you are trying to convey but could not let this pass without correction.


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## WizardDr (6 Nov 2018)

For the avoidance of doubt, the way the directive works is in fact solving for an 'r' and in the vast majority of cases this is monthly or weekly. There are the very few exceptional cases. In fact it is the IRR adjusted for an annualisation or the IRR in disguise.

I think the explanation  I gave by pinpointing for a sample year case is plainly correct and if you would like to review the Directive you would see that its merely presented differently. I assume even you accept that it is not a mere coincidence that my 'method'just happens to produce the same result.

What you should have said if you want to be helpful is that showing precisely an interest amount of €120.68 which is precisely 12.68% of €1,000 and is precisely the APR is the best clarity of what is a mystery for most people and it is not a coincidence or some subversion of the Directive.


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## Andrew Murphy (7 Nov 2018)

WizardDr said:


> For the avoidance of doubt, the way the directive works is in fact solving for an 'r' and in the vast majority of cases this is monthly or weekly.



This statement is rubbish, it is not how the directive formula works. What you are required to solve for is the 'Annual Percentage Rate' (hint, the period is in the title), where the sum of drawdowns equal the sum of financial and non-financial cashflows i.e. fees/charges, each discounted at the APR. The basis for measuring time intervals used in discounting each cashflow is detailed in the directive.

What should be apparent to you is the formula makes no assumptions as to the lender's interest rate, the interest compounding frequency (which may vary with the repayment frequency), the day calculation basis used, and so on. The only information required to perform the calculation are the value of cashflows and when they occur so the time intervals can be determined, be it days, weeks, months or years. That's all.

The beauty of the formula is it requires no advanced understanding of financial arithmetic to _check the APR_, just about anyone can do it. Finding the APR solution in the first place is a different matter altogether so I won't bore you with the details, suffice to say it involves iteration so you ought to
research the Bisection Method or the more efficient Newton's Method if you want to learn more.

Here's an APR proof based on one of your earlier examples of a €1000 loan repayable by 12 equal monthly repayments of €88.85 and an APR of 12.7%.

I've rearranged the EU directive algebraic formula to show that the net present value (NPV) of all cashflows is equal to 0, confirming the APR of 12.7% is correct (actually there is a slight discrepancy of 8c due to the loss of precision once the APR is rounded to 1 decimal place). Note the use of cashflow sign convention i.e. drawdowns are negative, repayment or payment of charges are positive.

NPV = (-1000.00 * (1+0.127)^-(0/12))
   + (88.85 * (1+0.127)^-(1/12))
   + (88.85 * (1+0.127)^-(2/12))
   + (88.85 * (1+0.127)^-(3/12))
   + (88.85 * (1+0.127)^-(4/12))
   + (88.85 * (1+0.127)^-(5/12))
   + (88.85 * (1+0.127)^-(6/12))
   + (88.85 * (1+0.127)^-(7/12))
   + (88.85 * (1+0.127)^-(8/12))
   + (88.85 * (1+0.127)^-(9/12))
   + (88.85 * (1+0.127)^-(10/12))
   + (88.85 * (1+0.127)^-(11/12))
   + (88.85 * (1+0.127)^-(12/12))

NPV =  -1000.00 + 87.97 + 87.10 + 86.23 + 85.38 + 84.53 + 83.69 + 82.86 + 82.04 + 81.23 + 80.42 + 79.63 + 78.84
NPV =  -0.08

I can already hear you asking why is any of this important if I get the same result using my own approach? Well it boils down to contract enforceability. If there are errors in the quoted APR a court may rule that a contract is unenforceable depending on the scale of error. From what I can ascertain the Irish legislation is silent on allowed tolerances, but in the UK where the same directive has been adopted an APR should not be understated by more then 0.1% or overstated by more than 1%. If it does the contract is non-complaint and hence unenforceable without a court order. The consequences to a lender of non-compliance can be severe.

As I said earlier, your approach can provide a good approximation, but that's all it is.

As this thread has gone way off topic this will be my last post on the APR issue.


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## RedOnion (7 Nov 2018)

Andrew Murphy said:


> This statement is rubbish, it is not how the directive formula works.


You're absolutely correct, but you're forgetting that in the simple world of Credit Unions, it's a perfectly valid approach, and the one taken in some of their IT systems... Therefore you're wrong!


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## WizardDr (8 Nov 2018)

I think we are at cross purposes here.

The EU calculator is itself an approximation. 

What we actually agreed on is that the payment profile is all that is required (I may have keyed in the wrong payment - in other words we will  both get the same result from the same payment - that is key)

For the avoidance of doubt again - you have to solve 'r' in any periodic payment profile 

Talking the monthly case, with no fees just interest - r is 1% then (1+r)^12 = 1.12685 which means APR is 12.685% or 12.7% to one place
That is how the maths work and if you read the EU calculator you will see the caveats in the calculation.

With the greatest respect that given the same payment profile then all that is different is the layout of the formula and by doing some further math one collapses into the other and actually are the same which is what I said originally. 

In other words you can end up with APR or with r and they are linked to each other so its working forward and back.

@RedOnion there is nothing simple about the systems, the issue is CUs do not debit the interest. That is the only difference between the systems. That by the way was the start of this.

Note: I don't use words that what you write is rubbish.I just happen to know why both are the same thing.


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## RedOnion (8 Nov 2018)

@WizardDr 
Apologies, I've reread my post and I never intended to imply here was anything simple about CU systems, so apologies if I caused offence to your work. I've seen the systems first hand.

But their products are simpler / more standardised than some bank products, where a purest approach has to be applied.


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## WizardDr (6 Dec 2018)

Thanks @RedOnion I was weary at the time.


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