DualCalc > Frequently Asked Questions

(Page last updated:  [insert date])

This page provides:

  • some FAQs on the program,
  • links to the Office's FAQs on the regulations themselves,
  • an explanation of the precedence of the Office's FAQs over these help files
  • clarification on one mathematical issue in the Office's FAQs, and

Please use the menu on the right to access the information you need.

If you have a question, please contact us by clicking here.



Brian Stewart
Office of Fair Trading



FAQs on the program ...

Currently we have only had a few FAQs about the program (and, in some cases, 'frequently' is frankly stretching things a bit).  Some of these are extracted from email or bulletin board exchanges and use some abreviations:

If these don't answer your question, please contact us by clicking here.



Complex Actuarial Calculations

Q.

... When I set the calculator to carry out a 'complex' rebate calculation using the actuarial system, it greys out the first two columns and I cannot enter different levels of repayments (or any repayment at all for that matter). Can you help?

A. 

That behaviour is intentional, since settlements dates are 28 days after whenever the borrower happens to ask for a statement - and since the lender can choose to use 30 days rather than 1 month as the deferment - we felt that settlement would not take place on a repayment date in most cases.

Because:

  • levels work in periods rather than dates;

  • our interpretation of the rules on calculating periods which are not whole weeks or months (ie you have to use years and days and take account of the changing number of days in a month, which in turn means you have to use dates to describe when things happen);

  • the fact that most loans have monthly repayments

... we felt that there was a twenty-nine in 30-ish chance that the user would be drawn into using levels in a non-statutory way - so they're switched off.

The correct approach in such cases is to use dates in 'Extras' to describe when the payments are made (with time periods set to Years&days and a relevant date entered). The 'Series' button saves you the fag of having to enter every date individually - in effect you can enter them as a 'levels-like' sequence of repayments (remember to set the period to 'months' and it will work out the dates taking account of the number of days in a month).

You can use regular repayments in a simple actuarial calculation, however this assumes you know that this is appropriate in terms of the timing - ie you know that the settlement date is a repayment date and the lender is using 1 month (or no) deferment, rather than 30 days.



Calculating Periods

Q.

I have an example of a loan for 80 being repaid over 28 days with a total repayment of 100, the APR quoted by the company is 1734, but, when I put it through the calculator with the 'periods in a year' field being 4 weeks I get an APR of 1719.

Does the 4 weeks refer to 28 days, as I am trying to understand how the trader could have come to their figure?

A.

The TCC Regulations define a week as a 1/52 of a year and what the program does when you select 'weeks' is calculate the weekly period rate for the loan and then convert it up to an annual rate by compounding the weekly rate 52 times. This is an easier way to do the calculation in a program and mathematically equivalent to directly calculating the annual rate using all the timings as 52nds of a year.

Similarly, when you choose the (technically, non-statutory) period of 4 weeks you used, it works out the four-weekly rate and then compounds it 13 times to get an annual rate. Not surprisingly, 4 weeks and one 4-week being the same thing, the final APR answer's the same too.  So 4 weeks is actually a 13th of a year rather than 28 days.

You can get a higher result using dates: I got 1737.2 APR for a loan on 1.1.06 repaid on 29.1.06 with 365.25 days in a year. You should get the same result for any 28-day period, the only thing which would change the result is using different values for 'days in year'. I've had a play around and my guess would be that the trader is:

  1. using dates 28 days apart;

  2. using 365 days in a year (wrong for the current TCC Regs, they should use 365.25 or 365 and 366) but it would be right for a pre-2000 TCC Regs calculation). This gives a result of 1733.5 APR;

  3. rounding the result to a whole number instead of 1dp - giving 1734

But I could be completely wrong, as their rate is relatively high, even trivial errors like these are going to take them outside the tolerances in the Adverts and Agreements Regs.

My guess is that yours is the right answer, although strictly with the periods set to weeks and the time of the payment set to 4. The TCC Regs say a period which is a whole number of weeks should be expressed in weeks and you should only use dates if it can't.



Checking Repayments

Q.

I've been asked by our local credit union to look at some loan examples they are using with prospective clients. One example is a loan with interest calculated on the decreasing balance. They want to use an APR so they can show clients how their loans compare with the local moneylenders and have calculated the weekly repayments to give them a target APR. How do I check their weekly repayments result using the DualCal program - I'm struggling because of the deceasing balance issue?

A.

As it stands DualCalc is not designed to do this type of thing. It's remit is just to do the statutory calculations, not provide a more general tool for analysing credit agreements, so it doesn't have a facility to calculate repayments.

You could of course just check the APR against the repayments by entering the loan details and seeing if you get the APR they think they're charging - the APR is an effective annual rate so it already takes the effect of a reducing balance into account.

You could also use the old DOS programs to do the repayment calculation (Schedule provides a facility to calculate the amount to pay off the loan by keying 'A' when you're entering the repayment, or MultiCal will do this too if you enter the other details and do a repayment calculation), or you could do it using an add-in Tool to DualCalc called 'Analyse' - see here for information on add-ins.

http://brian-stewart.members.beeb.net/credit/dualcalc/tools/index.htm



Accelerated or Late Repayments

Q.

I am currently attempting to check a settlement figure given to a consumer. The scenario is complex involving the consumer making payments over and above the required instalment during the course of the loan. How do I enter the two different sets of repayments to deal with this?

A.

The program doesn't provide a facility to enter two sets of repayments for one calculation (that's not a requirement of the statutory calculation), you would either have to do the calculation on the basis of what the borrower should have paid or what they actually paid, not both.

My understanding is that the Regulations (Reg.4(2)) permit the calculation to be done either way but, in a case of accelerated payments, the lender may well choose to use the contractual repayments and offer the correspondingly smaller rebate. See paras 19.32 and onward in the Office's FAQs on Early Settlement.

If you're trying to see the effect of the two different approaches (using actual or contractual repayments) you can simply do both calculations separately and compare the settlement figures.

Q.

I am able to do a Rule of 78 early settlement calculation with DualCalc where there are no arrears, but I am attempting to do a calculation where the debtor has made a number of payments either about 10 days late, or has paid only about 10 as a nominal sum.  I have found that whenever I have attempted to enter the details using levels, the program indicates that the charges are negative, which I note from the help pages means that the TAP is less than the total advanced. It also indicates that the deferred date is after the date of the last payment if I try to use extra payments.

A.

I get the same result and it's because the repayments you've specified add up to less than the loan.  I also get the report that the settlement time is after the end of the loan and that's because the last payment entered is at the same time as settlement.  It looks as though both these messages are being reported because you are only entering the repayments up to the time of settlement.  DualCalc needs to be told ALL the repayments over the whole term of the agreement, not just the ones actually made before settlement.

You're doing a Rule of 78 calculation using repayments which represent the actual payments the borrower has made rather than the ones set down in the agreement.  The provision which allows for calculations to be based on actual repayments rather than contractual ones (Reg.4(2)) only applies to the new actuarial calculation, not the old rule of 78 one.

A better approach with a Rule of 78 calculation would be to calculate the settlement figure based on the contractual repayments (ie assuming they were all made on time etc) and then separately try to assess the arrears and interest on arrears caused by the difference between what the borrower should have paid and what they really paid.  Unfortunately assessing arrears is beyond DualCalc's remit but you can use an add-in called 'Schedule' (based on one of the old DOS programs) for this type of thing.

Say someone has a loan of 6760.88 repaid by 48 monthly payments of 216.51 and an APR of 25.5.  If they settle at month 24 with 1 month's weighting the result is:

  Complex Rule of 78 Rebate Calculation
  Logged:  Fri.01 Sep 2006,16:34:10

  Loan Details:
  Loan Amount = 6760.88, (time = Zero)

  Days in a Year = 365.25
  Periods in a Year = Months
  Relevant Date = Zero

  Advance/Repayment Details:
  Levels = 1
  Level 1 = 216.51, Length = 48  (times 1 to 48)

  Early Settlement Details:
  Settlement Date = 24
  Deferment = 1 Month

  Rule of 78 Rebate Results:
  Loan Totals ...
  Total Amount Advanced = 6760.88
  Total Amount Payable = 10392.48  (TAP)
  Total Charge for Credit = 3631.60  (TCC)
  Rebate Results ...
  Total Remaining to be Paid = 5196.24
  Statutory Rebate of Charges = 852.31
  Final Settlement Amount = 4343.93
  Additional Information ...
  Total Paid Before Settlement = 5196.24
  Total Paid Including Settlement = 9540.17
  Settlement Plus Last Payment = 4560.44

So, assuming everything had been paid on time, the settlement figure would be 4343.93 (and the borrower should also make the 24th payment).

Now, to keep it simple, say they missed payments 5 to 10. Using Schedule you can come up with a figure for what the balance on the settlement date if they make all the payments would be (1.91248% is the monthly equivalent of the APR):

          Time    Per.Rate     Payment     Capital     Grs.Int      Remain
             0           -           -           -           -     6760.88
             1     1.91248      216.51       87.21      129.30     6673.67
             2     1.91248      216.51       88.88      127.63     6584.79
             3     1.91248      216.51       90.58      125.93     6494.22
             4     1.91248      216.51       92.31      124.20     6401.91
             5     1.91248      216.51       94.07      122.44     6307.83
             6     1.91248      216.51       95.87      120.64     6211.96
             7     1.91248      216.51       97.71      118.80     6114.25
             8     1.91248      216.51       99.58      116.93     6014.67
             9     1.91248      216.51      101.48      115.03     5913.19
            10     1.91248      216.51      103.42      113.09     5809.77
            11     1.91248      216.51      105.40      111.11     5704.37
            12     1.91248      216.51      107.42      109.09     5596.96
            13     1.91248      216.51      109.47      107.04     5487.49
            14     1.91248      216.51      111.56      104.95     5375.92
            15     1.91248      216.51      113.70      102.81     5262.23
            16     1.91248      216.51      115.87      100.64     5146.36
            17     1.91248      216.51      118.09       98.42     5028.27
            18     1.91248      216.51      120.35       96.16     4907.92
            19     1.91248      216.51      122.65       93.86     4785.28
            20     1.91248      216.51      124.99       91.52     4660.28
            21     1.91248      216.51      127.38       89.13     4532.90
            22     1.91248      216.51      129.82       86.69     4403.08
            23     1.91248      216.51      132.30       84.21     4270.78
            24     1.91248      216.51      134.83       81.68     4135.95

And a figure if they miss the six payments at months 5-10:

          Time    Per.Rate     Payment     Capital     Grs.Int      Remain
             0           -           -           -           -     6760.88
             1     1.91248      216.51       87.21      129.30     6673.67
             2     1.91248      216.51       88.88      127.63     6584.79
             3     1.91248      216.51       90.58      125.93     6494.22
             4     1.91248      216.51       92.31      124.20     6401.91

          Time    Per.Rate     Payment     Capital     Grs.Int      Remain
             5     1.91248        0.00     -122.44      122.44     6524.34
             6     1.91248        0.00     -124.78      124.78     6649.12
             7     1.91248        0.00     -127.16      127.16     6776.28
             8     1.91248        0.00     -129.60      129.60     6905.88
             9     1.91248        0.00     -132.07      132.07     7037.95
            10     1.91248        0.00     -134.60      134.60     7172.55

          Time    Per.Rate     Payment     Capital     Grs.Int      Remain
            11     1.91248      216.51       79.34      137.17     7093.21
            12     1.91248      216.51       80.85      135.66     7012.36
            13     1.91248      216.51       82.40      134.11     6929.96
            14     1.91248      216.51       83.98      132.53     6845.98
            15     1.91248      216.51       85.58      130.93     6760.40
            16     1.91248      216.51       87.22      129.29     6673.18
            17     1.91248      216.51       88.89      127.62     6584.30
            18     1.91248      216.51       90.59      125.92     6493.71
            19     1.91248      216.51       92.32      124.19     6401.39
            20     1.91248      216.51       94.08      122.43     6307.30
            21     1.91248      216.51       95.88      120.63     6211.42
            22     1.91248      216.51       97.72      118.79     6113.70
            23     1.91248      216.51       99.59      116.92     6014.12
            24     1.91248      216.51      101.49      115.02     5912.63

So the extra they owe because of the missed payments is 5912.63 - 4135.95 = 1776.68

And the total they owe to settle is 4343.93 + 1776.68 = 6,220.61 (or at least that's a reasonable estimate ... plus the 24th payment)

Trying to assess the effect of repayments which are, for example, made a few days late is even more difficult and would depend on the detailed terms of the agreement and the resulting accounting methods the lender uses.

One thing you could do is try to 'bracket' the likely result by first calculating the arrears assuming payments are made on time, which (unless the terms of the agrrment make it 'blidnd' to short periods of arrears) probably gives you a figure lower than the actual arrears, and then again assuming that anything made a little late is made a whole month late (if they're monthly repayments), which should definitely be more than the actual arrears.  The arrears charged should logically be somewhere between these two results.

You would then have to make a judgement as the whether the sum the borrower has been asked to repay looks about right (eg if most of the repayment were just a few days late it should probably be closer to the on-time rather than the month-late result ... but also remember that late payments early on in the agreement can have a bigger effect on the balance than those further on - because the balance and the interest charges are larger).  Based on that judgement and the sums involved (eg if the settlement amount is 20,000 is it worth querying something that might be 50 too high?), advise the borrower accordingly.  Remember, what you're doing here amount to checking the lender's accounting and application of the terms of the agreement, not the statutory calculation.

You can download a DualCalc friendly version of Schedule at the following link:

http://brian-stewart.members.beeb.net/credit/dualcalc/tools/index.htm



Agreements - Settlement Examples

Q.

We are a proprietary futures trading company who work within a bank. We are providing our employees and personnel with a facility to be loaned funds, our solicitors have prepared a fixed sum loan agreement which is regulated by the Consumer Credit Act 1974 and we now need to put some figures in the document.

We are granting 5 year (60 month) loan agreements with the first 6 months repayments deferred, i.e. zero.

Assuming the loan amount is 1000 and the rate of interest is 19.8% APR we need to calculate:

  • Monthly repayments (54 months) after the deferred period
  • Total amount payable

And also for the document amounts repayable if they exercise their right under section 94 to settle in full early on the first repayment date after the following dates:

  • On the date when a quarter of the term of the agreement elapses
  • On the date when half of the term of the agreement elapses
  • On the date when three quarters of the term of the agreement elapses

Can you help on this or give any pointers on how to use the DualCalc program to do this?

A.

The facilities to do all these calculations are actually already available to you if you have downloaded DualCalc, although I appreciate it would take a very detailed reading of the help files to realise this.

First, DualCalc will only do the statutory calculations of APR and rebates and your first step is to work out the repayments for the loan you describe.  Obviously this is ultimately the responsibility of the lender, but there is a reference to a small add-in for DualDalc called Analyse which you can read about and download here ...

http://brian-stewart.members.beeb.net/credit/dualcalc/tools/index.htm

... which should help you do this.  Alternatively, I suppose you could use DualCalc to 'fish' for the right repayment by setting up the repayment pattern and trying different repayment amounts until you get the right APR - but this is a bit more laborious.

I assume there are six monthly repayments of 'nothing' and the actual repayments occur seven to 60 months after the advance. I used Analyse to calculate the repayments as 29.84 a month which gives an effective rate of 19.8063038053% pa and, therefore, an APR of 19.8.  Note that in Analyse you should indicate that the first repayment is made after SEVEN months, but in DualCalc you would probably do an APR calculation by describing this as a loan with two 'Levels', the first being SIX repayments of nothing and the second 54 repayments of 29.84. The total amount payable will just be 54 x 29.84 assuming there are no other charges.

Turning to the three 1/4, 1/2 and 3/4 early settlement calculations, you could just use the program do these individually but DualCalc contains a tool to do all three of them for you.

Make sure the program is set to do a Complex Rebate calculation (the third and fourth buttons on the right - click them if they say something else - and that the Rebate method is set to Actuarial.

Now enter the details of your loan. Loan amount: 1000, Periods: Months, Days: 365.25 and enter the repayments. DualCalc won't let you use 'Levels' to describe the repayments in an actuarial calculation so you should use the 'Series' button to enter the repayments as 'Extras', click on it and enter the following in the dialogue ...

  • Amount: 29.84
  • Number: 54
  • First: 7
  • Interval: 1
  • Units: Periods

... and then click 'Add Extras' to enter all the repayments in the calculator.

Now click on the Tools button, in the first column of the Tools dialogue click on 'Early settlement examples', and then click 'Run Tool' underneath. There will be a large dialogue of information, the main point to note if you've followed the above is that you may receive some warnings - you will in this case but it's okay to use this method of describing the loan for example calculations because we are assuming that settlement takes place on a repayment date.

Click 'OK'. The program will do some checking and ask if you want to log the calculations. Click 'Yes'. The program will calculate the APR and then warn you that you should generally be using dates for the rebate calculations. Click 'OK' and you'll be asked to provide a filename to save the log.

The a log file containing the three calculations will appear. I got the following three settlement figures (DualCalc logs the latest calculation at the top of the file, so they're backwards):

  • 3/4: 403.42
  • 1/2: 725.56
  • 1/4: 982.58


The r-factor is not r

Q.

I have produced a detailed log of an actuarial calculation using the 'analyse' option but, as I understand it, the value for 'r' doesn't seem to be right. Is there a problem with the program?

A.

No. When providing a full analysis of an actuarial rule rebate calculation, DualCalc reports an 'r-factor' in its logs or printouts.  This is related to the value of 'r' in the statutory formula but is equal to 1 + r, NOT r (ie the value would be 1.011347621 in the period rate equivalent example given below). This is the value the program uses internally to do it's calculations, it isn't using the wrong value.



Converting Period Rates

Q.

I've used DualCalc's period rate convertor and it claims that 1% a month is 12.6825030132% a year.  Surely the answer should just be 12?

A.

That's understandable but the answer's no.  People often think in terms of what's known as 'nominal' rates where the period rate is just multipiled by the number of periods in a year to get an annual rate, so that they'll make your assumption, but the effective or compound annual rate, which assumes interest charged on interest, is actually around 12.68% pa because of interest charged on interest.  Just to provide a bit of background, an 'effective' annual rate is the one you get if you compound a period rate for each period throughout a year.

Take a loan where a loan where 100 is borrowed and interest is charged at 1% a month for 12 months, interest will compound as follows:

Month Balance (£) Interest (£) New balance (£)
1 100.00 1.00 101.00
2 101.00 1.01 102.01
3 102.01 1.02 103.03
4 103.03 1.03 104.06
5 104.06 1.04 105.10
6 105.10 1.05 106.15
7 106.15 1.06 107.21
8 107.21 1.07 108.29
9 108.29 1.08 109.37
10 109.37 1.09 110.46
11 110.46 1.10 111.57
12 111.57 1.12 112.68

As you can see the balance at the end of 12 months is £112.68 and the interest paid is therefore £12.68, the effective rate is 12.68% and the (rounded) APR is 12.7.

People sometimes look at this and say 'Hang on, what if I pay the interest every month?  Then the balance stays at £100, there is no interest charged on interest and I only pay 12 interest in total, so in that case, the rate must be 12%, right?'

Well, no.  It's true that the interest is only 12% of the capital, but an interest rate should reflect time as well as how much you pay.

If you pay the interest every month, you may have only paid £12 in interest, but you have also had to pay most of it sooner than the end of the year to avoid further interest being charged on it - so the effective annual rate at which you're paying interest is still the compound rate.  You've just traded time for money ... and the 'exchange rate' is the effective rate of the agreement.  The APR would only be 12.0 if the agreement required you to pay the £12 interest in one amount at the end of the year - and then the period rate would have to be less than 1%.

The formulae used in the conversions are quite straightforward:

    If i is the period rate, r is the annual rate and m is the number of periods in a year, then:

    r = 100 [ ( 1 +   i   ) m  - 1 ]
    100

    ... and ...

    i = 100 [ ( 1 +   r   ) 1/m  - 1 ]
    100

The first of these (or its equivalent) used to be a formula in the Total Charge for Credit Regulations.






FAQs on The Regulations ...

The Office has published a series of FAQs about the Regulations made under the Consumer Credit Act.  These include questions which cover the new requirements for the disclosure of APRs in credit agreements and the calculation of rebates under the new Early Settlement Regulations.  You can access the FAQs using the links below:

Please note:  in the case of any conflict between the information or views in these help pages and those in the Office's FAQs on the Regulations, the information in the FAQs (linked to below) should be regarded as the Office's authoritative view.

You can access the new Early Settlement Regulations on-line here:




'Period rate equivalent' ...

There is however a clarification to the draft FAQs on the 2004 Early Settlement Regulations which are important in relation to how the program does Actuarial Rule rebate calculations:

Question 19.32, "What is meant by 'periodic rate equivalent'?", says:  "The rebate formula includes the item 'r' which is defined as 'the periodic rate equivalent of the APR/100'.  To calculate this, start with the 'notional' APR as determined in accordance with Reg 1(2) (see Q19.27) and divide by 100.  This is then converted to a periodic rate equivalent."

The intention of the definition in the Regulations is that the value of r to be used in the calculation should be periodic rate equivalent of the (APR) and that periodic rate should be expressed as a decimal value rather than a percentage - a percentage value is, of course, converted to a decimal value by dividing it by 100.  This can be achieved either by the method described in Q19.32 - ie by first converting the APR to a decimal value and then finding the decimal periodic rate equivalent of that value, or alternatively, by first finding the percentage periodic rate equivalent of the APR and then converting that to a decimal value by dividing by 100 (this is what the program actually does).

It is important to note that dividing the APR by 100 and calculating the periodic equivalent as though it were a percentage rate will NOT give the correct value of r.

If the number of periods in a year, is 'm' (ie, if the periods are months, m = 12, if they are weeks, m = 52), the formula for calculating the decimal periodic rate equivalent of an APR expressed as a decimal value 'd' (which is APR/100) is:

( 1 + d ) 1/m  - 1

Alternatively, the equation for calculating the percentage periodic rate equivalent of an APR (which should then be converted to a decimal value) is the final formula given in FAQ on converting period rates, above.  Consequently, combining the two, r expressed as a decimal can be calculated directly from the APR expressed as a percentage with:

r = ( 1 +   APR   ) 1/m  - 1
100

For example, if the timings of the repayments of credit in the formula have been described using months and the APR is 14.5 then:

  r = ( 1 +   14.5   ) 1/12  - 1
  100
. r = ( 1.145 ) 0.83'  - 1
. .
. r = 0.011347621
. .

Please also note the information in the FAQ on the r-Factor, above.