# Banking StandardsWritten evidence from David John Pope

Simple interest causes un-necessary inaccuracy in banking.

Following the Commission’s initial response questions of 26 July 2012:

Question 1. The accuracy in modern UK savings interest calculation is in line with Babylonian standard (1700BC) when un-advertised simple interest (Actual/365) is used instead of advertised compound interest (AER). Simple and compound growths at 6% are indistinguishable at five significant figure accuracy but modern home computers can offer over 30 significant figures.

Question 2. The use of simple interest can lead to under-payment of interest to taxed savers and under-collection of tax revenue through TDSI for the same advertised AER. My personal worst example lost me £169.72 net (and HMRC one quarter of that) on a five year bond.

Question 3. My personal trust in the banking system has been shattered by the lack of systemic improvement from my 130+ letters about simple interest since 2005 (50+ letters have yet to receive a reply). I was very disappointed when The FOS sided with one of my providers that deducted over 21% of an equivalent tax free saver’s interest from my three year account. This was a consequence of using un-advertised simple interest in an account advertised with AER (a measure of proper compound interest). HMRC also lost out.

Question 4. The *existence* of simple interest in banking since 1803 is due to it not being banned when interest taxation at source was introduced. The Act of 1803 failed to define which interest was being taxed (simple or compound) despite previously published warnings about simple interest and the 1624 work of Henry Briggs that made the simple interest approximation to daily basis compound interest un-necessary. The *persistence* of simple interest may be due to lack of proficiency in maths in banking and the wider community, lack of a desire for achievable accuracy in senior banking management, the way that providers deliver simple interest without advertising it and HMRC’s failure to define which interest is being taxed.

Question 5. Simple interest (Actual/365) must be banned from all banking. Division by 366 with a rate based on 365 days must be banned from all banking. It is unfortunate that APR suffers from this day count defect in both its statutory and EC definitions. It is unfortunate that trade body code for savings suffers from both defects. It is important that AER does not go the same way on day count as existing APR when (if) it becomes defined by statute (or EC).

Question 6. The Financial Services Bill needs an amendment that bans simple interest and insists on proper compound interest throughout banking.

My summary points:

1.

2.

3.

4.

5.

6.

7.

(a)

(b)

(c)

(d)

8.

9.

10.

11.

(a)

(b)

(c)

12.

13.

14.

15.

16.

17.*The Envelope of Inaccuracy* is my name for the scatter of results due to simple interest, where proper compound interest would not have any scatter.

18.

19.

20.

21.

22.

(a)

(b)

(c)

(d)

£10,000x(1+0.8x5/100)^3=£11,248.64 which is £12.36 less than the fair net maturity.

(e)

(f)

100%x(£1,576.25-£1,248.64)/£1,576.25=20.784% by typical providers.

100%x(£1,576.25-£1,261.00)/£1,576.25=20.00% = Chancellors rate.

(g)

Year1: £10,000x5/100x0.8=£400.00 net interest, |
£10,000x5/100x0.2=£100.00 tax. |

Year2: £10,400x5/100x0.8=£416.00 net interest, |
£10,400x5/100x0.2=£104.00 tax. |

Year3: £10,816x5/100x0.8=£432.64 net interest, |
£10,816x5/100x0.2=£108.16 tax. |

Total net interest to saver=£1,248.64 |
Total tax to HMRC = £312.16 |

Proper tax would be 20% of the tax free saver’s interest = £1,576.25x0.2=£315.25 |

(h)

(i)

** My first reply from The BBA (in 2006) did not dispute this effect. After 19 letters to The BBA (the last 7 had no reply), 5 to The BSA and 10 to The FSA, simple interest still pollutes UK banking.

An example showing some of the weakness of the repeated Actual/365 method—the graphical version.

## ANALYSIS OF INTEREST CALCULATIONS ON SAVINGS

AUGUST 2012

## 17TH CENTURY TAX FREE INSIGHT EXTENDED

TO INTEREST TAXED AT SOURCE AND LEAP YEARS

For an advertised fixed rate AER/Gross over consecutive arbitrary time steps “days_{n}” the outcome by:

(1+Gross/100xdays_{1}/365)x(1+Gross/100xdays_{2}/365)x…

[Repeated Actual/365]

[Repeated simple interest]

in general is not equal to:

(1+Gross/100)^((days_{1}+days_{2}+…)/365)

[Time value of money]

[Compound interest, AER, APR, IRR, NPV...]

(From 1803) Taxation at source makes simple interest errors worse.

There is no mathematical need to prevent leap days from earning compound interest when a rate is based on 365 days.

In general:

Repeated simple interest fails to be proper compound interest.

Simple interest fails to deliver advertised AER.

Repeated simple interest fails to deliver 20.00% tax at source.

If this analysis is flawed then please tell me where.

If it is not flawed, then traditional inaccuracy can be avoided by eradicating simple interest and by including leap days as interest earning days.

*15 August 2012*

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