The flat rate trap

Before computers were used regularly, lenders had to rely on hand-calculated figures, and so they often looked for easy short cuts.  One such approach is still seen today and can be very misleading for short term loans unless you are wary.  It is the use of the so-called flat rate of interest.

Let us say a lender provided a loan of £1,000, to be repaid monthly over one year and simply quoted 14% pa as the interest rate, compounding annually.  You might be forgiven if you thought the following lender’s explanation of his calculation to seem fair.

14% of £1,000 is £140. So in one year, the amount lent including interest is £1,140.  If the loan is repaid in 12 equal monthly instalments, that works out to a twelfth of £1,140 each month which is £95 per month exactly, since 12 x 95 = 1,140.

This sounds like a straightforward loan @ 14% pa.  But the true annual rate in this example is actually 27.96 % pa, which is almost double the quoted rate.  This is because part of the monthly payment is actually repaying capital each month, so the capital debt is not £1,000 for the whole year.  The facile, flat rate calculation assumed interest was always charged on £1,000 as if it was outstanding for the whole year, when on average only about half of it was owed over the period.  Thus, the 14% quoted rate is about half the true rate.

The rate of interest of 14% used in this example is a flat rate.  The table in Figure 8 illustrates the schedule that amortises the loan if the true monthly interest rate is 2.0757 % or 27.96% pa true rate.

In reality, the interest each month is equal to the monthly rate (2.0757% pm) applied to the debt at the end of the previous month.  The debt at the end of each month is equal to the previous month’s debt plus interest for the month, less repayments made in the month.  Alternatively, current debt is the previous month’s debt less the capital element repaid – the calculation works out the same either way.

 

Figure 8

£1,000 loan over 12 months at 14% pa flat rate.

Month End

Repayment Made

Monthly interest rate

Interest Element

Capital Element

True Debt

Principal

 

 

 

 

£1,000

1

£95.00

2.0757 %

£20.76

£74.24

£925.76

2

£95.00

2.0757 %

£19.22

£75.78

£849.97

3

£95.00

2.0757 %

£17.64

£77.36

£772.62

4

£95.00

2.0757 %

£16.04

£78.96

£693.65

5

£95.00

2.0757 %

£14.40

£80.60

£613.05

6

£95.00

2.0757 %

£12.73

£82.27

£530.78

7

£95.00

2.0757 %

£11.02

£83.98

£446.80

8

£95.00

2.0757 %

£9.27

£85.73

£361.07

9

£95.00

2.0757 %

£7.49

£87.51

£273.57

10

£95.00

2.0757 %

£5.68

£89.32

£184.24

11

£95.00

2.0757 %

£3.82

£91.18

£93.07

12

£95.00

2.0757 %

£1.93

£93.07

£0.00

The true rate is 2.0757 % per month or 27.96% pa. - almost twice as high as that quoted!

 

Early redemption or settlement - the ‘Rule of 78’  
Flat rate loans sometimes suffer from another impediment:  the so called “rule of 78”.  Lenders using this rule (and they should state so in their literature) calculate the redemption figure (ie, the amount paid on early settlement) as simply the outstanding repayments.  So after month one in the example illustrated in Figure 9, there are eleven payments left:  so the actual amount owing is eleven times the monthly repayment of £95, which is £1,045 – yes it is actually more than you have borrowed!  It then reduces by £95 each month thereafter. 

The actual redemption amount owing for a “Rule of 78” loan - the same as that illustrated in Figure 8 - is shown in Figure 9 and compared with the proper, normal way of calculating redemption, by depreciating the balance as in Figure 8.  Clearly the rule of 78 disadvantages borrowers who redeem early and its only justification is its so-called “simplicity”.  Lenders who still use it for short term loans justify its use as covering the expenses of an early redemption, or early settlement.

The method used is described in the Technical Bits.  But suffice to say its name is derived from totalling up the first 12 numbers of a twelve month loan, ie 1 + 2+ 3 + 4 + … and so on:  it comes to 78.  This is also called the “Sum-of-the-Digits”.  The interest elements are then calculated as initially twelve seventy-eights, then next month as eleven seventy-eights and so on. 

Figure 9

Rule of 78 redemption compared with normal for £1,000 loan
over 12 months at a flat rate of 14% pa.

Month

Monthly

Rule 78

Normal

Difference

 

Payment

Redemption

Redemption

 

1

£95.00

£1,045.00

£925.76

£119.24

2

£95.00

£950.00

£849.97

£100.03

3

£95.00

£855.00

£772.62

£82.38

4

£95.00

£760.00

£693.65

£66.35

5

£95.00

£665.00

£613.05

£51.95

6

£95.00

£570.00

£530.78

£39.22

7

£95.00

£475.00

£446.80

£28.20

8

£95.00

£380.00

£361.07

£18.93

9

£95.00

£285.00

£273.57

£11.43

10

£95.00

£190.00

£184.24

£5.76

11

£95.00

£95.00

£93.07

£1.93

12

£95.00

£0.00

£0.00

£0.00

 

This rule is another hangover from the quill pen era. Nevertheless the Office of Fair Trading has outlawed this method for longer term mortgages, particularly non-status loans where one lender in particular abused it. The OFT will probably ban its use altogether eventually. However, a separate spreadsheet is included called “Rule of 78” for those interested in the technical calculations. Different lenders may interpret the calculations differently, often allowing an extra month or two to settle.

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