Of- T LIBRARY "^2 i UNIVERSITY OF CALIFORNIA. ^ GIFT OF A Received ccessions l 3/^^ .Shelf A -30 Mortality Experience of the Provident hife & Trust Company of Ph ila de Ip h ia. [UlTIVERSITYl Prepared by Asa S. Wing, Vice-President and Actuary of the Company. PiLblished by the Compciny, 1886. THE PROVIDENT LIFE AND TRUST COMPANY OF PHILADELPHIA. OFFICE: No. 409 Chestnut Street, Philadelphia, Pa. SAMUEL R. SHIPLEY, President. T. WISTAR BROWN, Vice-President. ASA S. WING, Vice-President and Actuary. JOSEPH ASHBROOK, Manager of Insurance Department. J. ROBERTS FOULKE, Trust Officer. DR. THOMAS WISTAR, Chief Medical E.Kami ncr. JOS. B. TOWNSEND, SAMUEL DICKSON, Legal Advisers. DIRECTORS. Samuel R. .Shu'i.ev, Philacklphia. Iskaki. Morris, Philadclphi:!. T. WisTAR Brown, Henry Haines, Richard Cadbuky, Richard Wood, William Hacker, Chas. Hartshornk, " William (Iummere, " Frederic Collins, " Murray Shipley, Cincinnati, Diiii Asa S. Winc, Philadelphia. J. Morton .Alberts; )N, Nonistown. Philii' C. Carkett, Philadelphia. Justus C. Sikawbridcje, Philadelphia. MORTALITY HXPERIENCH. In 1879 t^^'s Company published, in connection with its Fourteenth Annual Report, an exhibit of its mortality experience to the close of 1S77. That exhibit showed that the actual number of Policies terminated by death had been but 64. {'^f/, of the number expected by the American Table of Mortality, and that the actual amount of the Policies so terminated was but 65 /^^f of the probable amount by the same table. No such favorable Mortality experience has been published of any other Life Insurance Company in this Country. The late Elizur Wright said of it : " The mortuary experience of your Company, from 1866 to iS 77 inclusive, submitted to me tor my opinion, is a very remarkable and interest- ing document. That in an aggregate exposure, in the course of twelve years, of 46,539 years of life, between the ages of 1 1 and 76 inclusive, there should have been only 331 deaihs, when by the Table of lowest Mortality in use for Life Insurance 51 1 deaths were to be expected, is not perhaps wholly unprecedented but very uncommon. It indicates that either the selection of lives has been careful and judicious, or that the business has been sought chiefly among people of peculiarly good sanitary habits. I am inclined to think both causes have operated." 4 Provident Life and Triist Company. The limited space of twelve years through which that experience ran, and the comparatively small number of lives exposed, were the only factors in that exhibit which could take from its value as a safe comparison of the mortality experience of The Provident Life and Trust Company of Philadelphia with the published tables of mortality and with the experience of other Companies. The officers of the Company now present to its Policy holders an exhibit scarcely less favorable, with these possibly doubtful factors eliminated, showing the mor- tality experience of the Company to the close of 1885, It covers a period of 20 years, with 124,526 years of life and an amount of $380,334,659 j°^"^ exposed to risk in place of 46,539 years of life and $ 136,730,43 7, ^^ as shown in the former exhibit*. This experience covers a longer period and a larger number of exposures to risk than the experience upon which the x^merican Experience Table of Mortality was constructed by Shep- pard Homans in 1858. That these observations were sufficiently numerous and that the American Table is a fair exhibit of the general mortality of assured lives in this Country, is confirmed by the mortality experience of 30 American Companies collected by L. W. Meech and published in 1881. A comparison of the near rela- tion these two mortality tables bear to each other for each age is given in Table XVIII and more strikingly illustrated in Chart J. The accompanying explanations should be read in con- nection with the Tables and Charts submitted herewith. Provident Life and Trust Company. TABLE I. In the observations made for this and other Tables no account is taken of "Not Taken" Pohcies or those which lapsed in the calendar year of issue. Every policy (whether there be one or more upon the same life) issued and remaining in force at the end of the calendar year of issue is included in the exposures, and in the column of deaths the number of Policies terminated thereby is given without regard to the number of persons insured. These remarks apply as well to Tables III, V, VII and VIII. But in some of the other tables it will be noticed that observa- tions are made upon lives rather than upon policies. This table gives the probable and actual experience for each calendar year from 1866 to 1885 both inclusive. There were a few policies issued in the last half of 1865, but as they were so few and as there were no deaths in that year it was thought best to consider them as in force at the becrinninjif of 1866, and no credit is taken in the exposures for the time they were in force in 1865. Provident Life and Trust Company •-' >r" r^ O r-~ CO CT\ o M -t lO o n O O o M3 1^^ r^ I^ t~~ t^ 1^ t^ 11 CO «; CO 00 CO CO CO 00 00 CO CO I^ >-i o ,„_ rt 5 iJ \o ri CO O 'I- t^ r^ t^ o M ro 1— 1 O CO CN 1^ VO M -1- k-l o M to lO '^ UO r^ r-- CO o t-~ ■<^ O W--0 • o ■; o^ ^ 5 c u -' rt ^.s ■^ lO CO •Tf D O o o lO M r^ •^ p 1-1 O CO <-'^ ^r, •^ rO 'T ^ u S o ro r^ ro VO S-^ ^ "-' 1- o i^ h- 1 hri o o 1—1 r^ t-- O S "W3 o c ro i~~ CO o <-> VO CO M rO fO 00 O ro 6 Cs t-~ lO -O CN lO \j 'n ^ *■ M C4 CO fO -1- U-) o VO t^ ■$ S " 5 rt i; ||< o *"* i_ ■ . t; ■ 5 ^ — o £ a. in U-1 lO U-) o o m U-) o o O iJ ri CO ri Tt- -f 'i- ro CO r-^ 0 0\ Pl'O CNCOC^ O toOO 1-1 O t^OOOCOO lOVO CsN O u->T}-t-^o OO Tj-OOO I-^CnCnCnO 10 Probable Number to be terminated by death by the American Experience Table. t^-*0 CsM w ^O 't r-H- lof) r~~i-vDCO t-~ r^JOco CnO m roior^ ro M ■>*• Avcraj;e Nuiubcr of Tolicies Exposed. loO u-ju-jinO 6 lorots -^-CO rOror-» MO 10 n loroi-i 1-1 r) OOCO >-^oo r-co M u-)CN 00 r-~r^CO Cn>- rj ro — ►- i-i 10 "^ M 1^ t^CO 00 ►- ^J ro'^io t— t— r-^CCOOCOCOODCO cocoxoooocococooo Provident Life and Trust Company. TABLE II. This table represents in Dollars what Table I shows in Policies, and gives the gross expected loss as compared with the amount of Insurance terminated by death. For comparison, the result as thus arrived at is a fair one, but it must not be assumed that there was a eain to the com- pany of the difference between ^4,492,750, the probable loss, and ^3,085,55 1, the actual loss; for, strictly speaking, the amount exposed to risk is the face of the Policy less the reserve or accumulation thereon, and the real loss in case of death is the amount of the Policy less the reserve on it. If the computation had been made on that basis it would have shown a reduction in the probable and actual losses, but their relation to each other would not have differed materially from the ratio as shown in this table. No account is taken in the exposures or actual deaths of reversionary additions. They are small in amount and are accounted for in the Company's yearly computations of its gains on Vitality, but were not considered of suffi- cient importance to include in the present comparative statement. lO Provident Life and Trust Company H <■ l_J ii u l-H LJ > u C T' n < < < W w h :::; :^ < tin C Ch ■■§ 2 <.5 ro — <-a ^ = = ro O — o o o o lO u o M ^ (N U-) r~ r^ -+ 1-1 Cs M CO ^d O o CN CO \r '^ o CO o o o o o o o o CN rO CO o K- r^ Provident Life and Trnst Company, 1 1 r-. 'O CN o (M rO -t- >o rt ^•>» t^ r^ CO CO CO CO co CO ^ CO CO CO CO CO CO CO CO c/: c P -t CO '^ - C50 OO o M oc 00 CO G 11 •-. o q o q o O O q o q o q o q o lO o 2y H Providcul Life and I )ust Company. TABLE III. This table gives the experience for each age, showing the number of Pohcies actually terminated by death and the number expected to be terminated by the American Experience Table. The total result is of course the same as in Table I. The facts are graphically shown in Chart A, where the probable or expected deaths appear in the line at the outside limit of the blue color and the inside limit of the red, and the actual deaths are represented by the irregular lines bounding the buff, and the outside limit of the red. 14 JYovidcnt Life and Trust Company TABLE III.— {See Cluirl A) COMPARISON OK 'lllE ACTUAL AND PROBABLE NUMBER I'OLICIES TERMINATED BV DEATH. FOR EACH A(;i. OF riobuble Number to he Age Average terniinaled by death Actual Age at Niinil>cr of Poli- by the American Expe- Nunii)er at Exposure. cies Exposed. rience Table. terminated. Exposure. II •5 .004 II 12 I.O .C08 12 •3 2.0 •015 13 14 4.5 •034 14 15 16 1 1.0 .084 15 25-5 •195 2 16 17 43-a ■ZZ^ 17 18 82.5 .637 ]8 19 157-5 1.223 I '9 20 317-5 2.478 2 20 21 5^1-5 4.568 5 21 22 936-5 7-Z 46 47 2995.0 35-940 21 47 48 2819.0 ■ 35-263 10 48 49 2622.0 34.364 28 49 50 51 2410.5 33.219 30 50 2199.0 31.976 14 51 52 2035.0 31-317 19 52 53 1923.0 3T.408 29 53 54 1779-5 30-956 31 54 55 1620.0 30-085 22 55 56 1404.5 27.928 27 56 57 1261.0 26.903 15 57 5« 1 122.0 25.734 II 58 59 1004.0 24.819 14 59 60 861.5 22.996 12 60 61 733-5 21.183 13 61 62 646.5 20.230 8 62 63 5530 18.770 17 63 64 465.0 17.146 14 64 65 370.0 14.848 9 65 66 290.0 12.675 13 66 67 240.5 11-459 10 67 68 199.0 10.348 9 68 69 154-5 8.770 5 69 70 118.0 7-315 3 70 71 90-5 6.124 5 71 72 68.0 5-014 5 72 73 51-0 4.089 I 73 74 45 -o 3.916 2 74 75 33-5 3.161 7 75 76 18.0 1.842 I 76 77 15-0 1.666 2 77 78 II.O 1.329 78 79 8.5 I.I 20 79 80 4.0 ■578 80 81 3-0 .476 81 82 2.0 .348 I 82 Total, 124,526.0 1464.923 975 Toial. ■■ — ■— ▼■ o < 1 t^ X . r- a) o ; ojo (I'n -a-iqiun^^ < Providcul Life and Trus/ Company. 1 9 TABLE IV. This Table antl Chart B, show the corresponding facts as to probable and actual amount of loss in dollars that Fable III and Chart A show for the number of Policies. 20 Provident Life and Trust Company. TABLE W.— (Sec Chart B.) coMrARisoiN ()!• iiii'; .\( rr.\i. and i'Roi;a]!I.k amount termi- NATKI) \\\ I)1;AT11. FUR EACH ACE. \"C Probiihle Amount to \"L- Avcrai;(j Ainoiip.l be Icniiiiialcil by Aiitial Aniuunl ill Exposure. Exposed. death by American Experience Table. lerminaled. II $500.00 $3-758 II 12 1,000.00 7.543 12 13 2,000.00 15-138 13 1-4 9,000.00 68.364 14 IS 29,500.00 225.203 460.878 15 16 60,159.00 $2,000 . 16 17 95,818.00 736.649 17 18 171,715-50 1,326.845 18 19 337,800.50 2,623.021 1,000 19 20 766,208.50 5,980.257 11,533-826 2,000 20 21 21 1,468,342.00 11.500 2 2 2,489,056.00 19,678.477 30,500 • 2 2 23 3,740,555-00 29,767.337 26,564 -0 24 5,158,270.00 41,322.901 38,000 24 25 6,465,397-50 52,143.431 64,043-734 16,500 25 26 7,877,458.00 34,000 26 27 9,016,183.50 73,905-656 57,000 27 28 10,224,900.50 84,498.576 46,450 28 29 11,319,048.00 94,457-455 67,995 29 30 12,214,991.00 102,935.729 39,525 70,161 30 31 31 13,018,046.50 110,783-575 32 13,692,640.50 117,852.557 65,573 0- 33 14,506,122.50 126,464.375 113,670 v?3 34 14,909,175-00 131,662,924 70,300 34 3.S 14,934,384.00 133,602.999 66,691 88,008 35 36 36 14,950,803.00 135,887.848 37 14,841,648.50 137,047-782 69,437 37 3« 14,484,742.00 136,272.452 102,012 38 39 14,215,676.00 136,271.469 76,243 39 40 13,745,609.00 134,624.494 96,519 40 41 13,163,724.50 131,742.554 81,1 10 4' 42 12,411,245-50 127,240.085 87,783 42 43 1 ',793,291-00 124.030.038 112,429 43 44 11,047,286.50 119,631.064 91,796 44 45 10,836.591.50 120,968.870 88,66s 45 Provident Life a)id Trust ConipiDiy 21 TABLE \W.— {Continued. \ Age at Fiohahle Amount to A"i- ^Vvcrage Amount lie terminated by Aitual Amount at Exposure. ExjjObecJ. deatli by American Experience Table. Si 17,501.866 terminated. $1 21,300 Exposure. 46 $10,162,763.00 46 47 9,694,821.00 I '6,337-852 49,303 47 4'S 9,1 19,21 1. 00 114,072.210 36,000 48 49 8,461,864.00 110,901.189 85,707 49 50 7,690,299.00 105,980.010 90,285 50 51 7,018,502.00 102,056.038 50,091 5' 52 6,618,427.00 101,850.972 59,885 52 53 6,357,090-00 103,830.351 99,930 53 54 5,798,261.50 100,866.556 110,978 • • 54 55 56 5,281,717.00 98,086.766 90,839.581 62,128 55 56 4,568,246.50 65,833 57 3,965,561.00 84,605.244 65,750 57 5S 3,501,654-00 80,313-936 54,441 58 59 3,156,063.00 78,017.877 35,253 59 60 2,676,702.50 71,449-219 33,000 60 61 2,256,802.00 65,176.442 51,931 61 62 1,957,540.00 61,255.342 37,837 62 63 I 669,877.50 56,680.651 77,480 63 64 io75,577-oo 50,721.650 59,640 t 64 65 66 1,106,102.00 44,386.767 38,818.700 22,535 65 888,157.50 38,240 66 67 750,004 00 35,735-441 24,500 67 68 589,857.00 30,673-744 18,500 68 69 419,299-50 23,800.278 8,821 69 70 332,710.00 234,037-00 20,625.691 15,714.317 1 1,020 70 71 71 1 1,800 72 175,062.00 13,040.565 25,000 < . 72 73 127,397.00 10,214.437 1,000 73 74 115,195-00 10,025.190 1,282 74 75 91,965.00 8,678.829 11,650. 75 76 50,915.00 5.209.165 2,000 76 77 45,915-00 5,099 504 6,000 , 77 7'^ 33,835-00 4,088.182 78 79 24,335-00 3,205.747 79 80 10,835.00 1,565.289 80 Si 5,835-00 925.460 81 82 3,335-oo 581.280 $4,492,750,202 3,000 < $3,085,551 , 83 ■rut;l!. Total, S38o.334/>59-oo ,. . ^.. A. 1 a 1 -^ f* OS ti .S * P ^^ « -1 « i. D ^ o - m n ^ < o o e c • 6 o 1 6 o • IUU01.UV 6 < Provident Life and Trust Company. TABLES V and VI. In the Charts A and B, casual observers will probably be struck with the irregularity of the actual line of ckiath loss as compared with the probable. Tables V and W and Charts C and D are [)repared to smooth out those irregularities and to show the experience in groups of five ages instead of for each age. This gives an o])j)or- tunity for an average, and on the Charts the actual line presents a more regular appearance and falls within the probable line in all but one unimportant group. 26 Provident Life and Trusl Company a H r W I— 1 u h-1 a, r/f Uh W -^ o (^ < w w £0 > D f^H ^, fe o > " « -< -1 CP m < Pi h ^ Q ^ -< ^ ^. 1-1 o lo O lO O in o lO o lo O >r) o lO ri l-l o M3 i^ vq t--. vq vq l^ CO lO vq H w o Ci *J ^ O lO O O CO CO CO M lO CN " o o -1- m •^, = •+ 'CO o -t U-) ri M I^ vO -t r-» ■^ p M M 1—1 HH M CT» '^^ £ ^ _^ (t) ^H ^ ■~ ^ i> D ':=! o-^ S u-1 ■* U-) o o M „ „ ri O t~- r^ •+ CN ro ber eatl riei -+ vO CO VO t-H rO b^ CO -t CO r- VO O to M w CO CO 'Tt- On CO q M t^ ro y LT^/ CO ro O £- ?^ 4 •^ ro Xi-) M >.' lO l-O 00 1^' d ri r-^ ^ ,->.>< VO •+ O M o I^ LO M On LO ri VO '^.;f W 1-1 (S -l 1— 1 1— 1 ^ :^ 5 rt w ^ ti o Ki s - (i .^ (D ^^1 •r 'LJ O . "o . q q to O li-) q q q to q q q q to q Cs VO CO d M d c> "■o vo' fo CO ri co' i-i' vd l-c M \o t— • c^ r^ o o LO lO VO O CO VO 1*1 S o o^ o C/D -^ lO O^ o lo vq t--. q^ N lO <'l$ \o' t^ •■o ro <> -t Cs >0 ri' l-< -t- "^ r» M '^ ri X lo O io o >o O lO o lO O >o o lO M 1-1 ri l^l ro <-o -r -t >o lO VO VO I^ l^ CO , : il O O r;. O o o o o O O O Q ° - n -^ ■ ■^ ■^ p -1 O ■— ' O •—1 VO t— ' ^ - VO w VO « \o r~* I"! M i-O <-o 1- -t lo lo o VO t^ 1^ Pj^ovidcnt Life and Trust Company. E-" U U <: 2 •/ U1 o o O lo o lO O LO O lO PI )-H N M f-n PO -1- -t- LO lO lO ^ t^ r— X * 1) O o o o o o o o o o c o O o n <^ r^ M o »^ vO HN O " o ^-t o - o — o 1^ PI N PO PO -t- -t lO U-) O O r^ r^ 2 JJ O "^ * <1 o o PO PC U~> 11 l~-. o r^ O lO O M r^ 'z'2 ■^ o :o p« PO -f r^ u-> PI Cn r^- OC PO X •t- r^ UO >>c \o t^ \q I-^ o :o vq CC to O ^ Oi o ■z. o rt -^ '/> ^ ^ ~ — ■ o -t o in cr\ PO lO PI r^ PO - PI O i-i 5 5 o VO t^ o ^ cc o H- t^ PI cc PO o m - o q o_ a^ PO PI r^ lO q^ PI -r o t^ q^ uo < = vo CO -t o' PI t-i pf PO -t o - o ^- vo "S s W4 M -t y: PO.O cc cc lo -t O lO — 00 "s £ t-i PI PO 't -+ PO PO PJ PI WH q^ ■5 r^ CO -^^ m .' f' 5 i> "t; "•£75 — >^^ o O p) o o m - r^ PO r^ PI ■+ 00 r- PI 2": "^ o lO r^ lO PO -t - PI X <0 lO lO PO p) o o o Cn ^- -t- q o — vO X X cc PO sq p) = n.5 d r^ lO ►_■ o -f pj PO d vo d PO PO -f- d s^l N M -t -+ o o « o. c> PI PI U-) r-« r-» m ro t—i •+ -C^ PO _ vq^ t~- o^ P» f^^ o vq o r^ =V3, y^ -f' o> 6 O PO -f vo' lo cc" Cs r^ 6' C4 l-l U-) M cc w o o O r^ -+ U-! PI I-" •^ VO VO MD lO lO f M -^ "^ «.ii ^ "§•='5 m c" = c ^ < _ O o O o o O O o o O O O O o o 5 O 1J-) lO q lO IJ-) q q lO q lo q o q o Q d >-< d „' cc yi cs vi r^ t-^ X cc vd io Cs < 1 o o ri cc vO r^ ro lO C\ PI Cs PI to O 'O o^ t-~ O^ ^ PO t "^ Cn qv PI CC O so o sq ■J ~, rT 1^ IM pT o' zc pT OO' PO X to o PO to -f yjpr -i- . VO O X -t t^ ''O 2u ■m. -t 'V vo q^ PI PI l-l q^ 00^ PO C^ t~~ •-I PO •■J i_r C\ d ■_r pi c^ lO i_r rC ic pi d < to r~ r^ lo -t- PO tH 00 PO li-j o in o »r> O lO O m O lo O to M ri M PO "^ '1- -1- lO lO \0 VO r-» r~ oo o O O o O O O O 2 ° 2 O o ^ ^ O „ vO ^ O p- o „ o - o ^ o ^ PI PI "■O •-o -1- -f lO lO O vO r^ r- / / 1 / 'i •- .1 > 1 "^ 5 ^ ) ,.„ Z (";| noil fl ; .i>)<;|Uiii\- *'5 O CD ■dp*-' <, aj ^° P C • C cc 15 > ^ wi-i ^^ M Ti 1 Oi X ^ 0. Vj ^ H o-J n ,^ ;? r* ^ Cu 0) rO t:) cd >. E- X) o TT (13 0; C/D Cd Q >- H 0; ■j-i c: ^ ^ ^ n M-l (! J— o r- o ^ c ;: o >. i QQ '•5 1 i C ,3 CB 4: • -- - o g Q § 1 \ Provident Life and Trust Covipauy TABLE VII. In this table the Policies are arranoed so that observa- tions can be made upon them according to the length of time they have been in force. It will be seen that in the year of entrance the actual deaths are but Z^^-^'f of the probable, and that there is a regular increase in this per- centage until the third year, after which the ratios are more even. The figures will probably be better appre- ciated by reference to Chart E, where the red line repre- sents the expected mortality and the black line the actual, or perhaps it is still more plainly shown in Chart F where the red line is madct to represent the basis of ioo7' by the American Fable and the black line shows the percentage which the actual deaths bear to it. Care should be taken however in Chart F to compare it with Chart E, espec- ially in the striking case of the 19th year, where Chart F would seem to show that there was a very large excess in the actual result over the expected, but a reference to Table \\\ will show that it is only a difference of 3 policies, or a glance at Chart IC will discover the very small space between the expected and actual. To those familiar with such diagrams, this explanation is uncalled for, but casual observers should bear in mind in this and other charts that such irregularities are likely to occur when there are too few observations ox exposures to produce an average. 34 Provident Life and Trust Company, ^ 5 c o w w J i:' q ':^ o K . O PI ro -t lO VO r^ CO o O 1) >< O 5 • 5 ^ r— „ oo PI o P) r^ Cn -t- o t^ <| lO o\ CO r-- Cs Cs pi i^ LO PI CN rO -^ LO t^ r^ t^ r^ CO LO CO r^ ^ ^^ rt ^ .^ 5 -p _■ II fO ro )_< PI CO lO r-^ 1— 1 o -t ^O 'I- O o w C\ CO VD r^ -1- LO -+ •^ ■? ►^ •-1 '-' e a y !- ■C o o CO PO o -t lO -1- lO CO „ c ' c; CO r^ r^ o o CO o On lO o On "T -^ .i! rO ^O CO ON c> PO l-l t^ p< PO NO ^35 6 a-. iJ -f P-S r^ PI d p) LO r-^ PI o r^ -f pi' o o CO t^ o LO p "^ X CJ :2 ^I:i-i l^i-^ E ^ ?, t5 ">i: o >o LO q q LO lO >o S P> i^i -t c> C?N 6 -t o lO o t-^ On 1^ >— nj 1^ ri KH r^ lO o PI O PI Cn PO rj r-- -f- PO q ''I VO^ -1- "? t^ O ^ ^ N o' \o' PO ►H 6^ r^ o LO 't 'f ^ M l-l " '-' Provident Life and Trust Company 35 ~ rt t-i N rO -+ U-) \o t^ «3 Cv o o w »-( w H^ H^ ^ hH PI *Q >< o rt . *" 2 lj 5i O r^ r/^ >o 1— < CN 1-1 Cs r^ q MD u-j r^ Cn PI PI PO in O -f- vC O r^ O l^» ^q o o CO C\ vq "^ p ►,■ -" rt ^y •*^ OJ /3 • S 5 N '^j -t l-H -t- V-H CO o o o m fO r^ N P) 1-1 — r^ ■^1 CTi v! K u c: " — H ■L» ^ >. "-> r^-5^'-' M O P) Cs o r~- PI lO o PI CC CO CO PI ■*-* ^ (L> ri -t o Cn LO PI PI ^ q -t Cn 4> '« '^ S '^ X O M -f CO PI r^ PI t-^ PO T}- -1- -1- PO PI PI "" " y.-^ = ■Vj ?. « ■> ii o "?:«■%: ^ < 1 1 = 9 O U-) o U-) o lO o in q q q -J o d lO -f d I^ CC J. m' co' lO ^' ro ON CO o N O PI 1^ LO PI PI ro vq^ q^ o^ PI Cs o po lO ro pP pr ** — PI 0) .— •< ;S c rt 1-1 PI PO -if lO o r~- CO CN O "rt V •— ' ^— t-H N- HH k— M b« t^ N o ^ H I ^ ' \ 42 Provident Life and Iriist Couipany. TABLE VIII. In all the preceding- tables the American Tal)le of Mortality has been the basis for comparison, but in this the Combined Experience Table is substituted. This Mortality Table is used in many of the States as the standard for valuation of policies, notably when the re- serves are calculated with interest at 4'/ . it is designated by the several names: Combined Experience, Old Actu- aries', or I 7 British Offices Table. By a Comparison of the expected deaths with the actual it will be seen that in the youngest and oldest ages the ratio of actual deaths is larger, than is shown in Table V by the American Table, but that in the medium ages where most of the exposures occur the ratio of actual deaths is smaller, and that in the total result the actual deaths are but 61 ^\f/(, of the probable deaths by the Combined Experience Table, instead of 66,\% as shown in Table V by the American Experience Table. Provident Life and Trust Company 43 >^ w o y u „ ^- y. J b (^ m 2 o <: h ^ :?; n 1— 1 •^ < u w y. J ^ < Lj u < " lO O VO o »o O U-) O lO O "^ O >0 CI 1-1 M w fO ro '^f -t- m lo VO VO 1— t-~ X ^ o o o o O o o o o o o ° 2 2 o < w VO „ VO M VO „ VO *-■ VO 1- VO - VO H IH l-c N M rO ro 'i- ^ U-) irj vO vo r- t^ _o t^ . 2 ^ 5-^ o o ro lO o l-H C\ ro ro in ro CO lo 00 Cv • o o o h- 1 l-O o 1-1 ro ro Cs ro i^ -t- )-t h-< I^ lO lO VO I-~ VO VO to LO r^ CO LO VO '^^ ' HH o '-' rt « L4 1) -^ _-• C m ^1 O lO o o CO CO ro M lO Cn i-< o o 1- VO -^ CO o ■* u-i M w r^ O ^ (N 2 ~ i u o -J < - 6 ti OJ "rt -4=H '^ " (U -~ I^C '-J « o l_l r^ C) M r^ VO Ov O VO CO 00 f^ ^ ro D Ov CO es 1— 1 t~-. - rO O -t O VO O 00 Jl'l M IT) -f d 1- VO t-^ CO CJ 00 fT) q »o P ^ X lO -+ hH fO NH Cn CO 'I- O LO M t-^ 5 >>a " M N N M M H- 1-^ "? 12;-^ M iilc 1=1 p o ^ ^ 1 1 g o o o lO o LT) o q O lo O O O O LO o << I— Lij 0^ ° « On O CO d !_' d Os <■') O ro co' ri oo' 1-' vd H-l M o t— 1 Cs t^ o O lo lo O O CO VO (S VO lO to d^ 0_ >0 vO_^ t-^ -f C> LO N q N LO r^ -r; l-H M N ^^ H^ M ^ U o ^ •^ > o < (U »0 O »o O u-> O U-) O lo O lo O LO N 1-1 N M CO ro Tf 'i- lO LO VO VO t^ t^ 00 •« 60 o o o o O o O o o o o o o o "rt o < E_i M VO HH VO H-* VO ^rt VO M VO ■- VD - VO l-l l-H N M ro <-o -f "i- LO lo o VO t^ t^ 44 Provide III fj/c and Trusl Coinpiniy. TABLE IX. In this is presented a comparison of the actual amount of Insurance terminated by death, with the probable amount by the Combined Experience Table in (groups ot five ages. If this table is compared with Table VI it will be seen that by the Combined Experience Table the actual loss was but 63/5 % of the probable, and that by the American Experience Table it was 68/^ %. Tables Mil and IX are illustrated by Chart G, which shows the per- centages which the actual number and amount terminated by death bear to the expected number and amount by the Combined Experience Table. This Chart is also interesting as showing how nearly parallel the experience runs on the number of Policies, and the amount of Insurance. Providoil Life and Ti'itst Company 45 w — '-J '/ '/: ^ <^ T) Li V r. ^ ^< r ■J l-J 'vj X > c^ "U LJ 3 ^) <_r 1 X X ■r. x 1—4 " ' Cd i; '_, J < ^ OQ — z^ <: ^ X H X _:- 'J — ooooooooo r~^ t^ cc o o o — O i-HVO i-i\0 — O >-0 t-vO i-vo re -t fl X -I- CN VO o lO -+ O CO IJO r-^ yo tr CN O O ^ CN 'O -1- O '•r> lo <-o c- -t OD ijp o O NO U-1 NO U-) CC NO CO U-) NO O ^ O lO C\ ro u-> M r^ fO HH M o M o NO r--. ON ■-I 00 On 1^ t^ M CO <-o f> to C) C) On ro M r^ lO n M rj- o t-~ n lO >r) CO -t NO N ^ M ro -1- CN kH o HH 'yi M -t CO FO NO CO CO lO t () U-) HH 00 01 ro -t- ^ m ro CI r\ CO ro -t NO o CO lO NO CN >o o CN r^ -t O o r^ -f- CO CO NO Cn OC X> lO PI CN o M -1- NO NO r^ N -r Cn M o fO fO CN t^ NO -t ■+ 00 IT) rt- NO _ O 00 CN -t CO C) M 1— t •i- r^ lO U-) U-) o o NO M M "•O -t ^ —> lO )-^ U-) CN ri -^ U-) U-) ■«J- o r^ -1- lO irj Cn ». o NO O O CN O »-* -t — ro -^ NO -t- o NO NO u-> N 00 '-' -T *C r^ NO NO m -f "^ " Tt- m o O o o o O O O o O O o o O o -:i o m lO o >o to O O in O lO o o O o 3 o M o w CO CO CN CO r-~ r^ CO CO NO m CN 5 ~i o O INI CO NO t^ ro lO CN PI Cs PI in O in o r^ NO lO PO •i- (-1 CN CN PI CO () NO O NO -f ^. N I-. » PI o 00 o lO n lO o 'n o in o m PI .^• >-< ri ri "■o ro -r -f lO m •o NO I— 1^ CO ' u o O O o o o o o O o o o O o c; o <■ *"* * ■" ■^^ *^ '*-' ■*^ ■*"* '-' *^ *^ ■*"' * ■' *^ *-* 1-4 NO M NO ^ NO I-I o M NO 1-4 NO iM NO ' " ^^ M rl rr: T: -1- -1- lO in o NO r^ I^ ^i^ . ^^^-^^ .^<^>^ ^ \Sv H.' / ■v "\ •0 \ i "? l\ S \ / O / / ■>^ / s / s ^\\ ^ ^' A\ ,. < o\ ^ iN Ss \ '^ ^\ ■^ ^\ >; ■i: 1 :3 ^ • **■ « / 01 y r<:__ ^--==>-^ <^ ^ ■V Provident Life and Trust Company. 49 TABLE X. As heretofore explained the preceding tables so far as they relate to the mimbers at risk or members of deaths represent policies, but the Tables which follow deal with lives rather than policies. The usual methods have been adopted for counting- but once in the same year of ex- posure the same life, and the male and female lives have been separated. This Table represents the Experience of the Company on its male lives for each calendar year and corresponds to Table I as to policies. 50 lYoiudoit Life and Tnisl Company O Cri X w w w J '—> m y, <; h UJ VO t~-. CO ON o PI ri^ -+ lO, o rt O o o \o l^» t^ t^ r^ i^ 1 -^ o OO CO CO CO C/2 CO CO CO CO CO CO '<^ t— t ■^ ,__, 2 5 aJ CO o MD o _< r^ o „ to O o ■^■S lO CO' >o O o o K) I-- o o ro -t •^ vq o f~- CO LO vq ^ lO oOh 'Xj ca Pi . ;^ 0) J . s -^ ^1 -f ^ r^ po CO •+ PO CO r^ ■CO t~» i-i 1— t PI r/^ P) PO PI PO "rt ^^ 5 o o -> rj ij ^ r^ (U ^_ 5 3 ^ y r; O o PO o o o -t 1- PI t^ o •+ ro PI PI ''O PI m I^ PI *-H ^ fO o PO PI ^ Cn ^ CO t-^ o = -< g pi CO lO I-' 1^ -f d CO -+ c> lO •-- PI PI P'J -t- -i- lO lO o •^ ^ i *-. D ^ o zL ^• c ^ ■- o IJ Q_ iri q lO q q lO lO q q lO q "£ W "■O Cn !_' d Cn !_' PO "■o '■h d PI ^ Cn ri r^ -f >o 1^ CO f-i Cv CO -1- X p PI CO -+ q^ "? -,_ l-~. -t- CN *"? '^ ■i; -^ ^ pr PI PO r/^ -f -+ lO ir, |"'J O dj * u CO CO CO CO CO CO CO CO CO CO CO '.--' »— » . Provident Life and Trust Company. 51 r^ CO CN "- M fO 't >n _• t^i^i^cocococococo ^ c-: CO CO CO CO CO CO CO CO 1 ■ R tio of Actual to Proljable. 1^ CI PI CO CN "^ " fo -^ 5 — -l-OCO — ~. -or^VO 1■u-)•-^u-)^oo i^r-~co cji Probable Number of deaths by the .\merican Experience Table. 00 PI 10 C\ CO CO " >o C\ r^ — ro -1- " ro ir> M C^POO LOO r^PO-h co' PO co' C^ -' -f 1-^ 00 r^ t-^ CO CN — PI p'i M M Average Number of Male Live> Exposed. lo U-) 10 q in 10 10 U-) >n 0' — PO CO ro 1-^ in co' CN " t- - CN p» '+ ic m CO cc cs q 19 w o_ q -_^ in inmoor^cocso— -f -- - rt 1 r^ CO cs •- ""I PO •+ in — ' t— i^ I ~ CO CO CO CO CO CO '^ cococococococococo z Provident Life and Trust Company. 53 TABLE XI. In this table is shown the experience for each calendar year for female lives, corresponding to Table X for male lives. 54 Providcnl Life and l^rust Company. ^ S m :2:; w J c ^ ^1^ « M M lO O ir) I-. CO Provident Life and Trust Company. 55 t-~ CO C\ o M fo 't to rt t^ t^ r- CO CO CO CO oc 00 « ii 30 CO oc CO CO CO CO CO oo ,o K- ■^ "rt . Z3 u CO M -1- i-~ _ ri o •1- o o < "s ^ rg ^ 1^ o O CD r^ -t o o O iC lO o CO q t l^ CO <_ "o o 2 " ""■ " o '- rt Si V "^ y •^J U-) CO ^ ro o to (-~. ro o 1^ r: ;j ^ tr. rt o " ;^ ** ^— ^ --^ - !- « o VD -+ HH to to Cs lO t^ o — ^ (U »^ r) ^H o to <"0 to -t -t- I--. o CO C\ <^l o CI t^ rt q • - p -^ y ^ Tt- -f to \j~> o o t^ X CO s -. C 00 ^ D o ^ a- '^ *> >s rt- W J o iH Oh <-« O J I to lO q to q lO lO q q ro to 6s q Cs 5-: ^ •-^ o CO Cn o O Cn ro CO ^ >^ <" 2 rf rO ro ro 't Tf ^ to lO 00 — c U « X vr •3 -^ -r^ 1^ CO CN O M ro -+ >o rt t--. r^ t-^ CO CO CO CO CO CO "n CC CO CO CO CO CO CO CO oo r~ Provident Life and Trust Company. 57 TABLES XII and XIII. These Tables give in detail, the actual and probable deaths for male and female lives for each age. They are the basis from which a Mortality Table representing the Company's Experience has been prepared (see Table XVI). 58 Proi'idciLi Lijc and Irust Company. TABLE XII. ( ( iMl-AKlSOX OK Till-; ACIL'AI. AM) I'KnKAIU.l MALE LIVES '\:VA 34 4052.5 35-7«8 18 34 35 4062. 4047. 36.339 15 35 36 36-783 31 37 4009. 37.019 -7 ■> 37 3« 3^*9 1 - 36.607 27 38 39 379 '-5 36345 2 1 39 40 3668.5 35-929 24 40 41 3534. 35-368 19 4' 42 3320. 34-037 26 42 43 3124. 32-855 21 13 44 294«.5 31.92Q 24 44 45 2786.5 31.106 20 45 ( Continued on next page.) Provident Life and Trust Company 59 TABLE YA\.—[Conliimc;L) Age at Average Nunilier of Male Lives I'lohalilu Xuiiiber of (leatlis by the Actual Number of (leatlis. Age at Kxposure. Exposed. American Experience Table. Exposure. 46 46 -580.5 29.836 24 47 2457- 29.484 17 47 4 49 50 51 1980. i«23.5 27.286 23 1 1 50 51 26.516 52 1702. 26.192 17 52 53 1603.5 26.190 25 0.) 54 1492-5 25.964 24 54 55 56 1355-5 25-173 18 55 56 1187. 23.603 22 5 7 1072.5 22.882 14 57 5'^ 955-5 21.915 7 58 59 >S44.5 20.876 12 59 60 61 720.5 621. '9-232 17-934 10 60 II 61 62 '553-5 17.320 7 62 63 47T.5 16.004 15 63 64 39'''-5 14.694 13 64 65 312. 12.520 7 65 66 66 247-5 10.817 10 67 208. 9-911 9 67 68 172.5 8.970 9 68 69 134- 7.606 5 69 70 7' 100.5 6.230 _ 3 70 7' 78. 5-278 5 7- 59-5 4.387 4 72 73 43-5 3-488 1 73 74 3«- 3-3C7 2 74 75 27. 2.548 5 75 7^' '3- 1-330 76 77 12. 1-333 I 7- 7« 9- 1.087 78 79 6.5 .856 79 80 5- .722 80 81 3- .476 8t 82 Tntal, 2. •349. 1 ^2 104,588.0 1,229.770 796 ■r.it.ii. 6o JVovidciil Life and Trust Company. TABLE XIII. roMl'ARISON OF TIIK ACTUAI, AND PR( )i;Al!r,K NUMl'.KR OF FEMALE LIVES TKRMINATKl) i;\ Dl'.Alir. lOR KACII ACK at Exposui-e. Averai^e Number of Peinalc Lives Expt^sed. I'roliahlc Nunihei- of deaths by the Amerieaii Experience Table. .'\ctiial Nuinl)er i)f deaths. Age at Exposure. 13 14 15 16 17 . 18 19 20 I 2 5 5 5 .004 .01 1 .019 13 14 15 16 17 18 19 20 3 6 12 19 33 5 5 5 .027 .046 .097 •15^ .258 21 2 2 ^-3 24 25 26 27 28 29 30 49 63 79 94 103 5 5 .385 .502 .629 •753 ■S35 I I 2 2 21 22 23 24 25 III 129 157 179 193 5 5 .902 • 1.062 1.297 1.494 1. 631 2 2 I 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 ■i5 31 32 33 34 35 205 224 245 253 260 5 5 5 1-749 1.932 2.136 2.239 2.326 I 3 I I 2 36 37 3^ 39 40 255 259 253 252 252 5 5 2.322 2-3>2 2.380 2.416 2-473 3 I 2 5 41 42 43 44 45 232 223 215 215 212 5 2.322 2.286 2.266 2.328 2.366 2 I I 5 ( Continued on next page. ) Provident Life and Trust Company. 61 TABLE YA\\. — (Conli;iu,',> '•) Age at \ i\.T., , 1 «.. I'loliablc Number of FxDosed American Experience ot iieatns. ■v- Table. Age at Exposure. Exposure. 46 197. 1 2.278 3 46 47 190 1 2.280 I 47 48 173 5 2.170 48 49 170 2.228 4 49 50 157 5 2.171 2 50 51 51 140 5 , 2.043 52 120 5 1.854 52 53 113 5 1.854 I 53 54 98. 5 1-713 3 54 55 5^> 84 5 1569 I 55 56 76 5 1-521 3 57 71 1-515 57 5« 66 5 1-525 I 5« 59 61 1.508 59 60 61 54 5 1-455 ' 1 60 61 47 5 1.372 62 40 1.252 I G2 63 35 1. 188 I 63 64 30 1 . 1 06 I 64 ^'5 66 29 1. 164 t 65 23 5 1.027 2 66 67 16 .762 67 68 II -572 68 69 TO .568 69 70 71 7 5 ' -465 70 6 .406 71 72 3 .221 72 73 3 .240 73 74 3 .261 74 75 76 3 •5 -330 75 " 76 4 .409 I 77 3 •ZZl I 77 78 2 .242 78 79 Total, I .132 79 Total. 6849.0 83.770 67 FrovideiU Life and Trust Company. 6 o TABLES XIV and XV. In order to smooth out the irreg-ularlties which natu- rally occur in the experience for each age, tlie facts of Tables XII and XIII are now grouped in clusters of five ages each. These two tables are supplemented by Chart H, from which may be seen the relative line of Mortality for male and female lives as compared with the expected deaths by the American Table. No importance should be attached to the wide divergence of the actual and probable lines at the ends of the chart, for the reason 'given in explanation of Table \'II and Chart F. The divergerjce may be large in percentage but at the same time small in fact, as it is here, and as is quite likely to be the case where there are so few exposures. It is interesting to note the fact that the mortality on female lives is higher than on male lives. This is in accordance with most observations on assured female lives, notwith- standing that statistics show a higher death rate for men than for women in the general population. 64 Provident Life and Trust Company. tq c/5 ^ O ^ <: o>: M O D Cu, pa ^ ^ !^ o oi Q -< H U <: w m lO O U-) o m o lO O >o o to N ■ M N lO rO M* lO CO d oo CO CO Cs so o\ 3 >^? Tj- N 1— o o -1- CO O r^ -+ w « 2^W ■^ " •^ M " " " « — 5 M ^ u cs 'C ^ 0) O p ^ *: Ck < t: t, UJ (11 t/5 ^ o O lO lO q lO q q q q q to to o to q lO w fO i-~ d 1^ CO oo' t^ d so N so d oo' I-. ro 00 ^0 fo o 1-^ o r~- 00 to SO '^ to CO lO »1 rC Tj- M "i- 2 ►J 11 1-1 11 n n O — » S Si ?1 1% ^ O fe 1 ei t. 1 tJ o > ^ 'Ti X «* Ch ::i 3 u 2 o i-i CQ lo O lO li-i O to lo O u-> o to c< 11 N N ro ro ^ rr lo to o o f^ i~- 00 * so < o o O o o O ° 2 o o c o o o a ,o « vO t^ vo " VO w O 1- vo - Vil "H vo ^^ f< N ro ro -r '^ to to o o t— r^ "rt < 1 O T^ ro - 00 CO C\ ro to CO C\ O M o i_ O rt <^ CO r^ 1— 1 r^ CN to \o to CO Cv o ° "-o CN f^ r^ CN l>. CO to vo vo to I^ CO % ^ •^ - a f^ u U ^ £ u-' ,== ^ V <— — o o V3 in CO >-l Cs O to to •'^ f< O N 2 Q o < -C 1^ "% ^ O ,rt *■«.'" ■* Cn fO O N ro Cn t^ Tl- -f -^ ON vo o OJ QJ •-• ro r~ O CO CO CO O r) ro M CO 0\ to IH t^ 3 ^ X q lo I-; ro fO O up — q to q ro '^ ll r^ CO SO 6 » l-H la^ On f-- O ro -'' n' CO ^^W " " " « 00 M rt -^ .H rt I. ^ w 2 S =1- < •o u u n o O -a a. § W IT) U-) q O to q up q to to to q up q q crage N of le Lives rf- ^ ON d co" rj r^ co' t-^ cfN «" 00 00 d Cv t^ CO r^ CO t^ Cs 00 to f^ CO vo — rf ro t^ « N O. =<5 to ro >- oo^ vo" > « < S u tlH i/^ o \n O i^ lO o to O to O to N X fc- N N ro ro ■^ •* u^ to O O t-» r~ 00 r:" <; o o o O O O o o o o o o o o ,o w vo I-I vo « SO I-, o « O - vo - o f^ M r< ro ro -r -i- to lO O vO r^ r^ I Provident Life and Trust Company. 69 TABLE XVI. This is a mortality table constructed on the usual plan from the experience of the company on its male and female lives as given in detail for each age in Tables XII and XIII. As the company had so few exposures on lives younger than 15 and older than 75, the percentages of deaths for those ages were taken from the American Table in making up the unadjusted table. The unadjusted table was then graduated by the comparatively simple and very satisfactory method given by Mr. Woolhouse in the Journal of the Institute of Actuaries, Vol. 21, P. 45, etc., and the result obtained is set forth in this table. 70 Pi^ovidciit Life and Trust Company. TABLE XVI. MORTALITY TABLE, FOUNDED UPON THE EXPERIENCE OF THE PROVIDENT LIFE AND TRUST COMPANY, FOR MALE AND FEMALE LIVES. Age. Living. Deaths. dx Age. X. /-r. dx. Ix X. lO I 00000 579 .005790 10 II 99421 77^ .007825 II 12 98643 931 .009438 12 13 97712 1039 .010633 '3 14 96673 IIOI .011389 14 15 95572 1119 .011708 15 16 16 94453 1091 •OII55I 17 93362 1017 .010893 17 18 92345 89S .009724 18 19 9'447 566 .000189 19 20 90881 565 .006217 20 21 90316 554 .006131 21 22 88762 518 •005771 22 23 89244 503 .005636 23 24 88741 524 .005905 24 25 88217 454 .005146 25 26 26 ^7763 412 .004694 27 87351 399 .004568 27 28 86952 400 .004600 28 29 86552 414 .004783 29 30 86138 418 .004853 30 31 31 85720 430 .005016 32 85290 421 .004936 32 33 84869 415 .004890 2>i 34 84454 437 •005174 34 35 84017 4^5 .005416 35 36 83562 469 .005613 36 37 8J093 493 •005933 37 38 82600 522 .006320 38 39 82078 5" .006226 39 40 81567 534 .006547 40 41 81033 554 .006852 41 42 80479 564 .007008 42 43 79915 567 .007095 43 44 79348 610 .007688 44 45 78738 605 .007684 •007398 45 46 78133 578 46 47 77555 594 •007659 47 48 76961 625 .008 I 2 I ' 48 49 76336 606 •007939 49 50 75730 661 .008728 50 Provident Life a?id Trust Company. 71 TABLE XW I. —{Continued.) Age. Living. Deaths. dx Age. jr. U. dx. Ix X. 51 51 75069 790 .010524 52 74279 873 ■OII753 52 53 7340b 927 .OI262S 53 54 72479 1039 •014335 54 55 71440 1064 .014894 55 56 56 70376 972 .013811 57 69404 889 .012809 57 5« 68515 9J6 .013661 58 59 67579 866 .012814 59 60 61 66713 65806 907 .013596 60 1 108 .016837 61 62 64698 1 142 .017651 62 63 63556 • 1742 .027409 63 64 61814 1795 .029039 64 65 66 60019 2003 •033373 65 58016 2167 •037352 66 67 55849 2178 .038998 67 68 53671 2090 .038941 68 69 515^1 2102 .040751 69 70 7« 49479 47323 2156 2102 •043574 70 .044418 71 72 45221 2267 .050132 72 73 42954 2846 .066257 73 74 40108 3099 .077266 74 75 76 37009 3299 .089140 75 33710 3598 .106734 76 77 30112 3689 .122509 77 7'S 26423 3369 •127503 78 79 23054 3105 .134684 79 80 81 19949 2959 .148328 80 16990 2681 •157799 81 82 14309 2421 .169194 82 «3 1 1 888 2272 .I91117 ^Z 84 9616 2034 .211522 84 85 7582 1785 .235426 85 86 5797 1528 .263584 86 87 4269 1268 .297025 87 88 3001 1013 .337554 88 89 1988 769 ,386821 89 90 91 1219 670 549 •450371 90 361 .538806 91 92 309 212 .686084 92 93 97 68 .701031 93 94 29 25 .862069 94 95 4 4 1. 000000 95 Provident Life ajid Triist Company. jt, TABLE XVII. In this table is given a comparative exhibit of the Ex- pectation of Life by the Provident and other MortaHty Tables. It will be seen from it that if the present rate of mortality in The Provident Life and Trust Company is continued, the expectation of life of its members is much longer than by standard Mortality Tables. 74 Provident Life and Trust Co?npany. TABLE XVII. KXPI-:CTA'riON OF LIFK BV DIFFF.RENT MORTAIJTY T.\BLES. a 00 ■■J C V E V ritish es. 'Actuaries." ritish es. H. M. 'Actuaries." t) u H 5y [A V 1^ «E2 ""o^t " lO ^=2 faai M < to 49-99 £:-oo 80^ 6 < 10 52.20 48.80 48.72 48.36 50.29 48.82 II 51-50 47.97 48.08 49-32 47.68 49-54 48.04 II 12 50.90 47.12 47-45 48.64 47.01 48.73 47-27 12 1.3 5039 46.27 46.80 47-95 46.33 47.89 46.51 «3 M 49.92 45-43 46.16 47.26 45-64 47.03 45-75 14 15 i6 49-49 49.07 44.60 43-79 45.50 46.57 44.96 46.16 45-00 15 16 44.85 45.88 44.27 4529 44-27 17 48.64 4300 44.19 45-18 43.58 44-44 43-57 17 i8 4817 42.24 43 53 44.48 42.88 43-61 42.87 18 19 47.64 41.50 42.87 4378 42.19 42.82 42.17 19 20 21 46.93 46.22 40.7S 40.09 42.20 43-07 41.49 42.06 41.46 20 21 41.53 42.36 40.79 41.33 40.75 22 45-5' 39-43 40.85 41.65 40.09 40.60 40.04 22 2.3 44-77 38.78 40.17 40.93 39.39 39.88 39-31 23 2 + 44.02 38.15 39-49 40.21 38.68 39-15 38.59 24 25 43.28 37-53 38-81 39-49 37.98 38.41 37.86 25 26 42.50 36.92 38-12 38-77 37.27 37.66 37.14 26 27 41.70 36.31 37-43 38-04 36.56 36.91 36.41 27 28 40.88 35-71 36.73 37-31 35-86 30.16 35.69 28 29 40.07 35." 36.03 36.58 35.15 35-42 35.00 29 30 39.26 34.51 35-33 35-85 34-43 34.68 34-34 33-68 30 31 31 38.45 3.3.92 34.63 35-12 33.72 33.95 32 37-64 33-32 33-92 34-38 33-01 33.21 33-03 32 33 36.83 32.72 33-21 33-65 32.30 32.48 32.36 33 34 36.00 32.12 32.50 32.91 31-58 31-75 3.. 68 34 3'^ 36 35-19 31-52 3178 31.07 32.17 30.87 31.02 31.00 35 3b 34.38 30.92 31-43 30.15 30.29 3032 37 33-57 30.32 30.35 30.70 29.44 29.56 29.64 37 3« • 32-77 29.71 29.62 29.96 28.72 28.84 28.96 38 3' 31 97 29.10 28.90 29.22 28.00 28.12 28.28 39 40 41 31-17 28.49 27.87 28.18 28.48 27-75 27.28 26.56 27.40 27 61 40 41 30-37 27-45 2668 26.97 42 29.58 27.25 26.92 27.01 25.84 25.96 26.34 42 43 2878 26.62 26.00 26.28 25.12 25.23 2571 43 44 27.98 25.99 25.27 25-55 24.40 24-5' 25.09 44 45 46 27.20 25.36 24.54 24.82 24.09 23.69 23-79 23.08 24.46 23.82 45 46 26.40 24.71 23.81 2297 47 25.60 24.06 23.08 23-38 22.27 22.38 23-17 47 48 24.79 23.40 22.36 22.66 21.56 21.68 22.50 48 49 23-99 22.74 21.63 21.95 20.87 20.99 2I.8I 49 50 23-13 22.08 20.91 21.24 20.18 20.31 21. II 50 Provident Life and Tntst Company. TABLE yj^\\.—{ Continued.) 75 !> A i M. ries." £" c -il ■^^1 •S<2 ^0 u . 51 0^ So < ^0 ^00 u 22.38 21 41 20 20 20.54 19.50 19-63 20.39 51 52 21 61 20.75 19.49 19.84 18.82 18.95 19.68 52 53 20.86 20.09 1879 19.15 18.16 18.28 18.97 53 54 20.12 »9-43 18.09 18.47 17.50 17.62 18.28 54 55 19.41 1S.78 18.13 1740 17.80 16.S6 16.96 16.32 17.58 55 56 18.69 16.72 17.13 16.22 16.89 56 57 17-95 17.49 16.05 1647 1559 15.68 16.21 57 5« 17.17 16.87 15-39 15-83 1497 15.05 15-55 58 59 16.40 16.25 14-74 i5-'9 14-37 14.44 14.92 59 bo 61 15.61 14.82 15.64 14.10 13-47 14.56 13-94 13-77 1383 14.34 60 1)T 1505 13-18 13.24 13.82 62 14.06 14-47 12.86 13-34 12.61 12.66 13-31 62 ^l m^ 13.90 12 26 12.74 12.05 12.10 12.81 63 64 12 67 1334 11.67 12.16 11.51 11.55 1230 64 b5 12.03 12.80 11.10 11.60 11.04 10.97 10.46 II.OI 11.79 65 66 "•43 12.27 10.54 10.49 11.27 66 67 10.86 11-75 10.00 10.50 9.96 9.98 10.75 67 68 10.28 ir.25 9-47 9-97 9-47 9.48 10.23 68 69 9.67 10.76 8.97 9.46 9.00 8.98 9.70 69 70 71 9.06 10.29 8.48 8.00^ 8-97 8.54 8.50 9.18 70 8.45 9.83 849 8.10 8.03 8.65 71 72 7.82 9-39 7-55 8.02 767 7.58 8.16 72 73 7.21 8.97 7.11 7.57 7.26 7-15 772 73 74 6.69 S.56 6.68 7.14 6.86 ^.75 7.33 74 75 76 6.20 576 8.18 6.27 6.72 6.48 6.38 7.01 75 7.81 5.88 6.32 6.11 6.02 6.69 76 77 5-39 7-45 5-49 5-93 5-76 5.67 6.40 77 7« 507 7.12 5-" 5-57 5-42 5-34 6.12 78 79 4-74 6.80 4.74 5-21 5-09 5-03 5.80 79 80 4-39 6.49 4-39 4.87 4-55 4.78 4.72 5-51 80 81 4.08 6.20 4-05 4-48 443 5.21 82 3-75 5-93 3-7« 4.24 4.18 4-17 4-93 82 «3 3-41 5.67 3-39 3 95 393 3 93 4.65 83 84 299 5-42 308 367 3(^^ 3.71 4.39 84 «5 86 2.79 2.50 518 2.77 3-40 3-3(> 3-51 4.12 85 4 95 2.47 3-14 3.10 3-31 3.90 86 »7 2.22 4-74 218 2.89 284 3.10 371 87 88 1.94 4.54 1.91 2.64 2-59 2.88 3 59 88 89 1.67 4-34 1.66 2-39 2-35 2.63 3-47 89 90 1.41 4.16 1.42 1. 19 2.17 1.98 2.11 2.36 3-28 3-26 90 91 91 i'5 3-98 1.89 208 92 .92 3-8i .98 1.81 1.67 1.80 3-37 92 93 .84 3.65 .80 1.64 1-47 I. SO 3-48 93 94 .64 ' 3-49 ■64 1.49 1.28 1.20 3-53 94 95 .50 3 ..U .50 Ij4 1. 12 •93 3 53 95 Provident Lije and Trust Company. 'j'] TABLE XVIII. If in any Mortality Table the number dying at any age is divided by the number living at that age the result gives the percentage of death by that table for that age. It is generally represented by the expression ^_^. Taking the ^? for each ao-e bv the American Table as shown in Table XVIII for a standard, we have placed side by side the per- centages which the probability of death (^^'■) by the Provi- dent and other Mortality Tables bear to it. The result is given in Chart J, in such a way as to show at a glance the comparative rate of Mortality by the several tables. 78 Pi'ovidcnt Life and Trust Company, TABLE^ XVIII.— (5f^ Chart J.) PERCENTAGE OF MORTALITY {^\l) BY THE AMERICAN TABLE, AND THE RATIO WHICH THE PERCENTAGES OF MOR- TALITY BY OTHER TABLES BEAR TO IT. dx ix ^y Ratic of . to that of the American Table. 20 British Age. American Table. Provident, 1S66 to 30 American Offices, 17 British Offices, Old "Ac- Offices, H. M., New "Ac- Carlisle. Age. 1885. Meech. tuaries." tuaries." 25 .008065 .638 .872 •963 .822 .907 25 26 .008130 .577 .875 .970 .822 .906 26 27 .008197 •557 .877 .977 .S42 .948 27 28 .008264 •557 .880 •985 .868 1.052 28 29 .008345 •573 .885 .992 .896 1.178 29 30 .008427 •576 .888 1. 000 .916 1.199 3'^ 31 .008510 •589 •893 i.ooS •930 1. 199 31 32 .008607 •573 .898 1. 016 .942 1.(77 32 33 .008718 .562 •903 1.023 •950 '•153 Z2> 34 .008831 .586 .909 1.030 •963 1. 149 34 35 .008946 .605 .914 1.038 .981 i.m6 35 36 .009089 .618 •923 1.044 1.002 i.i6t 36 37 .009234 •643 •930 1.049 1.025 1. 176 37 38 .009408 .672 •938 1.05 1 1.040 ..187 38 39 .009586 .649 •947 1.057 1.052 1.239 39 40 .009794 .668 •956 1.058 1.052 1.328 40 41 .010008 .685 .964 1.060 1.048 1^376 41 42 .010232 .684 •975 1.063 1.047 1.402 42 43 .010517 •675 •984 1.070 1.058 1.387 43 44 .010829 .710 •994 1.080 1.067 1^367 44 45 .01 1163 .688 1.004 1.094 1.092 1.327 45 46 .01 1562 .640 1. 01 1 I.I 10 1. 119 1. 281 46 47 .01 2000 .638 1. 019 1. 126 1. 142 1.217 47 48 .012509 .649 1.024 1. 140 1. 154 1.114 48 49 .013106 .606 1.027 1.149 1. 161 1.044 49 50 .013781 •633 1.028 1-157 '••57 •974 50 Provident Life and Trust Company. 79 TABLE yiVlW.- {Continued.) Ralie J of . lo that of the American Table. American 20 British Age. Provident, 1866 30 American 17 British Offices, Offices, H. M. Carlisle. Age. Table. to Offices, Old "Ac- New "Ac- 1885. Meech. tuaries." tuaries." 5^ .014541 .724 1.028 1. 162 1. 146 •983 51 52 .015389 .764 1.028 1. 166 1. 1 40 .988 52 53 •016333 •773 1.026 1. 1 69 ^•139 .989 53 54 .017396 .824 1.022 1. 168 ^•134 .971 54 55 .018571 ,802 1. 019 1. 167 ^■^Zl •965 55 56 .019885 •695 1. 014 1. 163 1. 129 •955 56 57 •021335 ,600 1 .01 1 ^•157 1. 124 •979 57 58 .022936 •596 1.005 1. 150 1. 117 ••055 58 59 .024720 .518 •999 ^•143 1.114 1. 144 59 60 .026693 •509 •994 1. 136 I.l 12 '•255 60 61 .028880 .583 .988 I.I 29 1. 109 1.239 61 62 .031292 .564 .981 1. 122 1. 107 ^•i95 62 ^Z •033943 .807 •975 1. 115 1. 104 1,127 63 64 .036873 ,788 .969 1. 107 1.098 1.079 64 65 .040129 .832 •963 1.099 1.082 1.024 65 66 •043707 •855 •956 1.C89 1.065 .972 66 67 .047647 .818 •950 1.080 1.047 •932 67 68 .052002 •749 •943 1.070 1 .024 •893 68 69 .056762 .718 •938 '•059 l.OIO .S65 69 70 .061993 •703 •932 1,047 1.003 .833 70 71 .067665 .656 .928 1.037 1.006 ,870 71 72 •073733 ,680 •925 1.028 I.0I6 .924 72 73 .080178 .826 •925 1. 021 ^•033 •974 73 74 .0S7028 .888 .927 1. 017 1.048 1.036 74 75 .094371 •945 •930 1.013 1.042 1.012 75 Provident Life and Trust Company. 83 We give below, for comparison, the result of some of the observations made by other companies as well as Ratio of Actual to Probable Loss by the Combined Ex. or OU Actuaries-' Table. our own : Mutual Life of N. Y. 1843- -1873- Ratio of Actual 10 Probable Loss by the American Table. / On Lives, f •799 C©«necticut) Mutual. 1 846-1 878. On Policies, .856 On Amount, .879 On Lives, .853 On Male Lives, .846- On Female Lives, -945 Mutual Benefit. 1845-1879. On Lives, .848 On Amount- .S94 -778 Michigan Mutual. 1867-1881. On Policies and Lives, .765 .709 John Hancock, 1863-1883. On Lives, .732 On Female Lives, .823 On Amount, .843 Penn Mutual. 18 74-1 885. On Amount, .785 Provident Life and Trust Company. 1 866-1 885. On Lives, On Male Lives, On Female Lives, On Policies, .666 .619 On Amount ^,m,^ '"— -^j^w -^87 .637 84 Provident Life and Trust Company. It is not likely that any one cause can be assigned which will fully account for the unusually low rate of mortality shown by the experience of The Provident Like and Trust Company of Philadelphia. There must however be some satisfactory explanation for facts borne out so uniformly year after year. In the early history of the Company it was supposed that so laroi'e a number of insurances upon members of the Society of Friends would have a favorable effect upon the average vitality of the Company, on account of their well known reputation for longevity; but as the Company has increased in membership the proportion of Friends among the insured has become small, and the experience of the Company has shown no corres- pondingly increasing rate of mortality; so that while the insurances upon the lives of Friends may have con- tributed somewhat toward the favorable result attained, we cannot consider it as an important factor. The large proportion of new insurances written by this Company each year, as compared with the amount already in force, would naturally have a favorable effect upon the mortality experience ; for all companies of good standing will show a rate of mortality much below any standard general expectation, during the first three or four years of the existence of the policies; but that this fact does not give a satisfactory explanation lor the exceptionally low death rate in the Provident is shown by throwing out of this Company's experience the years of exposure o, i and 2 (see Table VII), that is those especially favored by recent medical examinations, and the remaining years will still show a death rate of only 75 \o'/^ o^ die American Table, which is below the rate Provident Life and Trust Company, 85 that other companies (which have published statistics of their mortahty) show for their whole experience, inckid- ing the most favorable years of exposure. After a careful observation of the tables presented herewith, we are of opinion that the three principal causes which have contributed to such a favorable ex- perience in this Company, are those which have been alluded to several times in our Annual Reports in com- menting upon the continued exemption of the Company from a high rate of mortality : First: The character of the agents who secure the business, anci their conscientious devotion to the best interests of the Company whose reputation they have done so much to establish. Second : The ability and care of our medical exami- ners, and especially of the Chief Medical Examiner, who passes upon all cases before they are accepted by the Company. Third: The limitation of our business to the more healthful sections of the country. V' f I.' /t ?(*■ j v/v '^ Vfc ""ill 3f- '■4 ^i" .•E x>. 0'^ 3I' >> y^. 4^ fe. - 1 2I2S7 Ha. 8785 /S35