The
flat rate trap
Before
computers were used regularly, lenders had to rely on handcalculated 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 socalled 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.
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
socalled “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 “SumoftheDigits”. The
interest elements are then calculated as initially twelve seventyeights, then
next month as eleven seventyeights and so on.
Figure 9  
Rule
of 78 redemption compared with normal for £1,000 loan 

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 nonstatus 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.