The Law Commission



APPENDIX F

CALCULATING COMPOUND INTEREST FROM TABLES

F1.     In Part VI we recommended that the Court Service should produce multiplier tables to be used to calculate compound interest where the parties do not have access to a computer. We envisage that such tables will be particularly useful in the court corridor and the court room.
F2.     Here we illustrate what these tables might look like. During consultation we were keen to ensure that tables would be easy to use and given an acceptable level of accuracy. We therefore showed these tables to four county court kudges, who all thought that such tables would be useful.
F3.     An important aspect of the tables is that they should specify each detail of the calculations, as even minor variations in calculation methods can lead to noticeably different results. Differences can arise for example, with even minor variations – whether, for example, February is treated as a twelfth of a year or 28 out of 365 days. Another difference is whether one uses "set date" or "anniversary" compounding. With annual compounding it can make a crucial difference whether one compounds on a set date each year (such as 1 January) or on the anniversary of the debt arising. With monthly compounding the difference is less, but still noticeable. We recommend that anniversary compounding is used as it eliminates one of the sources of inaccuracy noted in paragraph F7 below and allows easier and more accurate calculations of parts of the month.
F4.     Table 1 below demonstrates what a compound interest multiplier tables might look like, though for convenience it only shows the first 6 months. The annual interest rate figures taken in calculation of the multipliers are 2002 at 4%, 2003 at 5%, 2004 at 4%, 2005 at 4%, 2006 at 5% and 2007 at 5%.

TABLE 1: COMPOUND INTEREST MULTIPLIERS AT ANNUALLY VARIABLE RATES USING MONTHLY RESTS

2002-2007

	Jan07	Feb07	Mar07	Apr07	May07	June07	July07	Aug07	Sept07	Oct07	Nov07	Dec07
Jan02	1.2456	1.2508	1.2560	1.2612	1.2665	1.2717	1.2770	1.2824	1.2877	1.2931	1.2985	1.3039
Feb02	1.2414	1.2466	1.2518	1.2570	1.2623	1.2675	1.2728	1.2781	1.2834	1.2888	1.2941	1.2995
Mar02	1.2373	1.2425	1.2476	1.2528	1.2581	1.2633	1.2686	1.2738	1.2791	1.2844	1.2898	1.2952
Apr02	1.2332	1.2382	1.2435	1.2487	1.2539	1.2591	1.2643	1.2696	1.2749	1.2802	1.2856	1.2909
May02	1.2291	1.2342	1.2394	1.2445	1.2497	1.2549	1.2601	1.2654	1.2707	1.2760	1.2813	1.2866
June02	1.2250	1.2301	1.2352	1.2404	1.2456	1.2508	1.2560	1.2612	1.2665	1.2717	1.2770	1.2823

USING THE TABLE

F5.     In order to understand the effect of the table, it useful to take an example. Assume that £100,000 has been owed from 11 March 2002 – 17 June 2007, with interest fluctuating as listed above.
F6.     The rough table calculation may therefore be done as follows:

Figure given by table from March 2002 – June 2007 = 1.2633.

£100,000 x £1.2633 = £126,330.00

This compares with the pure maths calculation, which gives a final figure of £126,433.80. The table gives a figure that is around £100 less, which we consider to be acceptably accurate on a £100,000 loss over a five-year period.

F7.     The discrepancy in the figures arises in two ways. Firstly the rough month based multipliers take no account of the number of days involved at the start and end of the compounding period. In the example given above the multiplier from March to June does not take account of the days between 12-17 June 2007. If set date compounding were used then the multipliers fail to take the periods 1-11 March and 17-30 June into account. The more significant of these two discrepancies would be the original one as it immediately inserts inaccuracies into the calculation which are then compounded. However anniversary compounding eliminates this discrepancy.
F8.     Secondly the month-based figures take no account of the exact number of days to be calculated, but only the round month figure. In the example given above there is a discrepancy of 6 days away from the round month figure (11 March – 17 June). Six days at 5% per annum of £126,000 is itself £103, which accounts for much of the discrepancy.
F9.     The multipliers can obviously be used with a little common sense such that if a period ends on the last day of the month the multiplier for the next month is a more appropriate one to use. At the extreme, the multipliers may provide a figure £500 away from the pure maths figure on £100,000 over five years. This does not seem an unacceptable amount.
F10.     A further advantage of using the anniversary compounding process is that fractions of the figures given in the tables can be used to gain a more accurate figure. For example, using the same figures as above:

(1) Multiplier for 11 March 2002 – 11 June 2007 = 1.2633 x £100,000 = £126,330.

(2) Multiplier for March 2002 – July 2007 = 1.2686.

(3) 6 Days in June 2007 = (1.2686 – 1.2633) x 6/30 x £126330 = £133.91

TOTAL = £126,463.91.

F11.     The tables provided will not be able to cope with calculations if judges vary the rates away from those specified. Whilst it is possible to publish multiplier tables to cover a variety of plausible situations, the resources required to cover all the possible options are simply too great. Parties who are applying for a variation in the rate will need access to a computer to carry out the calculations.

CONTINUOUS LOSS

F12.     Continuing future loss does not attract interest so is of no concern here. Continuous loss over a past period does attract interest, and we recommend that that interest be compounded. Although the traditional method of calculating continuous loss does not apply to compound interest it is mathematically possible to do it accurately. The calculation is relatively simple provided the interest rate does not fluctuate. If it does then the simple calculation becomes impossible. However, table multipliers can again be used.
F13.     The tables produced will be in a similar format to those used above. An example is reproduced at Table 2 below, using the same annual interest rates as have been used in the above examples. To use it, one multiples the average monthly loss by the multiplier given.

TABLE 2: COMPOUND INTEREST CONTINUING LOSS MULTIPLIERS AT ANNUALLY VARIABLE RATES USING MONTHLY RESTS

2002-2007

	Jan 07	Feb 07	Ma r07	Apr 07	May 07	June 07	July 07	Aug 07	Sept 07	Oct 07	Nov 07	Dec 07
Jan 02	67.352	68.636	69.927	71.222	72.523	73.829	75.141	76.458	77.781	79.109	80.443	81.783
Feb 02	66.106	67.386	68.671	69.961	71.257	72.558	73.864	75.176	76.493	77.816	79.145	80.479
Mar 02	64.865	66.139	67.419	68.704	69.994	71.290	72.591	73.898	75.210	76.528	77.851	79.179
Apr 02	63.627	64.897	66.171	67.451	68.736	70.027	71.323	72.624	73.931	75.243	76.561	77.884
May 02	62.394	63.658	64.928	66.202	67.482	68.768	70.058	71.354	72.656	73.963	75.275	76.593
June 02	61.165	62.424	63.688	64.958	66.233	67.513	68.798	70.089	71.385	72.687	73.994	75.306

F14.     The table covers cases where interest is awarded at the specified rate for damages that are assumed to have arisen evenly over time. Even where the losses are not completely even, it is common for them to be treated as even for interest purposes. Where losses consist of discrete items, or where another interest rate is used, the parties will need to use the computer programme