6 -
7. It will be observed that the contributions at first largely excued the pension payments, but that the contrary is the case after 15 years. The interest at 6 per cent has by that time become a valuable auxiliary to the income from contributions, and the Fund continues to increase until it amounts to Rs 21,391 at the time when the members having attained age 65 all
income from contributions ceases,
8. By a separate calculation it has been ascertained that the actuarial value at + per cent interest of («) the pensions current at the end of the period of 30 years and (2) the prospective pensions on account of the surviving members, together equal Rs 21,391 which shows that the Fund might be expected to exactly meet all pension payments up to the cessation of the last pension.
9. Columns are added showing the position if interest be earned at 3 per cent per annum and also if no interest be credited to the Fund. In the former case the Fund at the end of the 30 years is considerably short of the amount required to meet the future pensiou payments, even if the rate of interest were then increased to 6 per cent; and obviously if only 3 per cent interest were earned by the Find after the contributions ceased, a much larger sum than Rs 21,391 would be necessary to provide for the future pension
payments.
10. The columm hended - Fund without interest" shows that on this assumption the pension payments could not be met in full after the 28th year, and that when all contributions ind reased there would be no assets of any kind to meet the large payments falling due for pensions.
11. The last column of Appendix A shows the percentage of the income from contributions and interest at 6 per cent absorbed by the pension payments. It will be observed that this percentage increases steadily year by year.
12. lu Appendix B is set out for each year from the commencement of the Ceylon Widows' and Orphans' Pension Find the percentage of the actual yearly income from contributions and interest absorbed by the actual pension payments of the year. This percentage, like that described in the preceding paragraph, shows a distinct tendency to increase; not indeed with the same rapidity and regularity because no new members are assumed to enter the Fund of Appendix A whereas in the case of the actual experience of the Ceylon Faud, set out in Appendix B, the percentage column is affected by the constant introduction of new contributors. It will be at once seen that although the Ceylon Fund has been in existence for 20 years yet the average period for which the present inembers have belonged to the Fund is very much less than 20 years, a considerable number of them having in fact entered during the last 10 years. Bearing this in mind and noting also that the actual experience of the Ceylon Fund as a whole might be analysed into 20 partial experiences, if separite accounts were kept, for the members who entered in each of the 20 years of its existence, and that each of such partial experiences would be similar in type to the experience of the Fund of Appendix A it is obvious that the Fund as a whole is working normally. It will also be apparent that the percentage of the income from contributions and interest which is absorbed by the pension payments will continue to increase as the average duration of membership grows larger, and as the number of members aged over 65 years increases.
13. Summing up the considerations presented in paragaphs to 12 above it may be confidently stated that if the Fund be continued on its present basis, the annual addition marle to the corpus will tend to diminish, and that eventually the pension payments will exceed the receipts from contributions, aul the income from interest will become a vital necessity to the preservation of the Fund. Should the rate of interest earned fall materially below 6 per cent the Fund will be unable to meet in full the pension payments calculated by the present Tables.
14. The assumptions upon which the arithmetical illustrations in the Report by the Directors dated 16th March last are based are in our opinion as Actuaries acquainted with the practical and prolonged working of Widows' Pension Funds, entirely crroneous.
For we must obviously regard the Fund in relation to its capacity of ultimately fulfilling all its existing contracts, and not simply in respect of any specific date, especially in the early stages of its history.
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15. The proposed return of the interest each year as bonus obviously annuls accumula- tion at compound interest and thus effectively prevents the final satisfaction of the obligations. Compound interest is as essential, in all Funds with prospective liabilities as appropriate rates of nortality, and the very pensious incorporate in the arithmetica! illustration assume the operation of compound interest as the indispensable condition of their maintenance.
16. It is stated by the Directors that we expressed a judgment that at the end of two decades the Ceylon Fund will have reached its umaximum of pension expenditure. No such opinion has been submitted by us. If the admission of new contributors ceased it would be possible to estimate approximately the date at which the pension payments might be expected to attain a maximum amount, but the Ceylon Fund is constantly recruited by new entrants in numbers that vary considerably from year to year, and the total membership has largely increased as will be seen from the following figures:-
No. of contributors at end of 1884.
1889..
1894.
1899..
1903.
..1,075
..2.195
.3.07%
.4,039
.4,592
It is obvious that each increase of membership tends to defer the date at which the various items of the Fund's accounts will attain a position of stable equilibrium. As explained in parapraph 12 above, the average perio of membership of the present n tributors cannot be very great.
17. Referring to the calculations in paragraph 13 of the Directors' Report, where an annual increase in the pension payments of Rs 7,000 is assumed which gives an increase over a period of 10 years of Rs 385,000, it may be well to point out that by doubling this last amount and allowing for an increase of Rs 770,000 during the following 10 years, the annual increase during the second period is not Rs 14,000 as might be supposed from a hasty perusal of the Report. This is evident from the following statement :--
Approximate pensions for year 1905 according to new Tables........... Rs 104,000
Pensions for year 1904 if increase be Rs 7,000..
ני
111,000
Do,
1905
clo.
13
118,000
Do
1906
lo.
12
125,000
Do.
1907
do.
132,000
Do.
1908
do.
139,000
Do.
1909
lo.
77
146,000
Do.
1910
dlo.
39
153,00K)
Do.
1911
do.
160,000
Do.
1912
D
1913
do. lo.
167,000
3:
174,000
Total for 10 years 1904-13
Rs 1,425,000
Pensions for
year 1914 if increase be Rs 14,000........
R 188.000
Do.
1915
lo,
19
202,000
Do.
1916
do.
*
216,000
Do.
1917
dlo.
+1
230,000
Do.
1918
do.
11
244,000
Do.
1919
do.
37
258,000
Do.
1920
lo.
272,000
Do.
1921
do.
17
286,000
Do.
1922
da.
300,000
12
Do.
1923
do.
314,000
11
Total for 10 years 1914-23
Rs 2,510,000
1,085,000
The total for the second decade is greater by
34
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