Daftar Pustaka Bowers, N., Gerber, H., Hickman, J.C., Jones, D.A., and Nesbitt, C. (1997) "Actuarial Mathematics", 2nd ed., Schaumburg, IL: Society of Actuaries. Howard E., Winklevoss, PhD., "Pension Mathematics With Numerical Illustrations", Associate Professor Of Insurance And Actuarial Science Wharton School. Jordan Jr., Chester Walace, 1967, "Life Contingencies", The Society of Actuaries. Peraturan Perundangan, Keputusan Menteri Keuangan Republik Indonesia, No : KEP-194 / KM.6 / 2004 tentang Pengesahan atas Peraturan Dana Pensiun dari Dana Pensiun Karyawan Taspen. Takashi Futami, "Actuarial Mathematics Part I", The Research Institute Of Life Insurance Welfare, Japan. Takashi Futami, "Actuarial Mathematics Part II", The Research Institute Of Life Insurance Welfare, Japan.
29
Lampiran 1 Tabel mortality cso80 lx (i) –––––––
qx (i) –––—
9958200.00000
0.00107
8948737.26600
0.00099
8042319.66833
0.00098
7227793.53232
0.00095
6495979.43717
0.00090
5838586.31813
0.00086
5247954.92619
0.00080
4717386.68315
0.00076
4240647.58495
0.00074
3812172.55297
0.00073
3427028.75994
0.00077
3080658.96317
0.00085
2769050.30905
0.00099
2488573.20325
0.00115
2236107.45178
0.00133
2008851.85145
0.00151
1804330.64446
0.00167
1620343.04864
0.00178
1454938.43024
0.00186 30
LAMPIRAN 1
31
1306301.92020
0.00190
1172797.86396
0.00191
1052926.19428
0.00189
945327.66649
0.00186
848752.99208
0.00182
762078.33653
0.00177
684293.00072
0.00173
614474.58586
0.00171
551792.03335
0.00170
495509.24595
0.00171
444962.34777
0.00173
421721.96435
0.00178
399674.34005
0.00183
378759.38184
0.00191
358908.60263
0.00200
340065.90100
0.00211
328976.35196
0.00224
318205.66620
0.00240
307736.69978
0.00258
297556.76975
0.00279
287651.10489
0.00302
280741.72535
0.00329
273922.50884
0.00356
267194.97202
0.00387
260549.83307
0.00419
253986.58277
0.00455
246481.27925
0.00492
239106.55938
0.00532
231856.84850
0.00574
224729.56898
0.00621
LAMPIRAN 1
32
217715.75913
0.00671
209723.41361
0.00730
203997.96442
0.00796
198294.18133
0.00871
192601.15539
0.00956
186907.86523
0.01047
179343.70393
0.01146
173701.55100
0.01249
168057.98761
0.01359
162412.91981
0.01477
156765.82258
0.01608
151109.71171
0.01754
145437.05313
0.01919
139737.37502
0.02106
133999.75840
0.02314
128219.00882
0.02542
122395.30144
0.02785
116538.68627
0.03044
110660.47493
0.03319
104774.44427
0.03617
98889.26373
0.03951
93004.36365
0.04330
87117.18743
0.04765
81223.70970
0.05264
75323.61943
0.05819
69434.06563
0.06419
63588.41164
0.07053
57831.75273
0.07712
52215.13291
0.08390
46789.98060
0.09105
LAMPIRAN 1
33
41593.95325
0.09884
36650.92785
0.10748
31978.66757
0.11725
27589.59544
0.12826
23499.16202
0.14025
19733.42131
0.15295
16320.52609
0.16609
13283.43939
0.17955
10632.72906
0.19327
8365.08693
0.20729
6463.78633
0.22177
4901.03671
0.23698
3641.56829
0.25345
2645.78144
0.27211
1872.92223
0.29590
1281.26609
0.32996
832.87421
0.38455
495.93495
0.48020
247.86829
0.65798
79.81855
1.00000
Lampiran 2 Tabel Gam83 untuk program pensiun lx (i) –––––1000000.00 999658.00 999340.11 999038.31 998744.59 998452.96 998160.41 997862.96 997559.61 997250.37 996934.24 996610.23 996278.36 995936.64 995585.07 995221.68 994846.49 994456.51 994050.77
34
LAMPIRAN 2 993629.29 993188.12 992727.28 992242.83 991733.81 991196.29 990629.32 990028.01 989389.44 988709.73 987984.02 987208.45 986359.45 985464.83 984512.87 983489.96 982380.58 981164.39 979820.20 978324.01 976646.19 974759.31 972631.41 970228.04 967521.10 964485.02 961096.78 957339.85 953200.32 948667.85
35
LAMPIRAN 2 943734.78 938393.24 932639.95 926467.74 919853.68 912753.33 905100.81 896811.90 887786.38 877902.66 867024.56 855000.67 841669.50 826873.79 810498.38 792481.81 772814.79 751539.20 728726.98 704409.36 678571.62 651165.47 622125.45 591399.92 559016.04 525096.06 489848.99 453565.88 416607.51 379396.13
36
LAMPIRAN 2 342395.52 306085.51 270935.87 237293.76 205527.25 175916.32 148674.09 123948.55 101859.18 82459.08 65719.31 51398.81 39367.07 29586.87 21777.30 15662.17 10976.77 7473.15 4924.15 3126.58 1897.51 1086.79 576.51 275.60 113.96 38.15 9.15
37
Lampiran 3 Program Quick Basic untuk Pensiun Plan –––––––––––––––––––– DEFDBL A-Z CLS DIM lxa(111), lx(105), qxc(105), qxw(105), ax(111), qxm(105) DIM PVPENCAT(100), PVPENJND(100), PVPENYTM(100), PVPENCPT(100), PVPENTUNDA(100) DIM PVFB(100), MATI(100), KELUAR(100) DIM PVPENS(100), PVFP(100), PVPENNT(100), ALAKTIF(100) DIM PVPENSDRP(100), PVPENJNDP(100), PVPENYTMP(100), ALPENSIUNAN(100) DIM PVSDRTUNDA(100), PVJNDTUNDA(100), PVYTMTUNDA(100), ALTUNDA(100) DIM cso80ml(100, 2) ’*** Asumsi Aktuaria *** bu = .105 v = 1 / (1 + bu) skl = .03 OPEN "i", #1, "D:\safari\gam83.txt" FOR i = 5 TO 105 INPUT #1, lxa(i) NEXT i
38
LAMPIRAN 3 CLOSE #1 FOR i = 5 TO 110 FOR j = 0 TO 105 - i ax(i) = ax(i) + v ^j * lxa(i + j) / lxa(i) NEXT j NEXT i OPEN "i", #2, "D:\safari\cso80ml.csv" FOR i = 1 TO 99 INPUT #2, cso80ml(i, 1), cso80ml(i, 2) lx(i) = cso80ml(i, 1) qxm(i) = cso80ml(i, 2) ’PRINT i, lx(i), qxm(i) NEXT i CLOSE #2 ’INPUT b$ FOR i = 0 TO 99 IF i <= 29 THEN qxc(i) = 3 / 10000 qxw(i) = 10 / 100 END IF IF i >= 30 AND i < 35 THEN qxc(i) = 5 / 10000 qxw(i) = 5 / 100 END IF IF i >= 35 AND i < 40 THEN qxc(i) = 5 / 10000 qxw(i) = 3 / 100 END IF IF i >= 40 AND i < 45 THEN qxc(i) = 10 / 10000
39
LAMPIRAN 3
40
qxw(i) = 2 / 100 END IF IF i >= 45 AND i < 50 THEN qxc(i) = 50 / 10000 qxw(i) = 2 / 100 END IF IF i >= 50 AND i < 51 THEN qxc(i) = 100 / 10000 qxw(i) = 2 / 100 END IF IF i >= 51 AND i < 55 THEN qxc(i) = 100 / 10000 qxw(i) = 1 / 100 END IF IF i >= 55 AND i < 56 THEN qxc(i) = 200 / 10000 qxw(i) = 1 / 100 END IF IF i >= 56 THEN qxc(i) = 200 / 10000 qxw(i) = 0 END IF NEXT i ’*** PERHITUNGAN KEWAJIBAN AKTUARIA *** ’*** BAGI PEGAWAI AKTIF *** OPEN "d:\safari\PENS2005.prn" FOR RANDOM AS #1 LEN = 45 FIELD #1, 12 AS NIK$, 1 AS sex$, 2 AS tgllhr$, 2 AS blnlhr$, 4 AS thnlhr$, 2 AS tglmi$, 2 AS blnmi$, 4 AS thnmi$, 7 AS phdp$, 3 AS sts$, 5 AS mk$ pegawai = 2032 peg0 = 0
LAMPIRAN 3
41
FOR i = 1 TO pegawai GET #1, i tgllhr = VAL(tgllhr$) blnlhr = VAL(blnlhr$) thnlhr = VAL(thnlhr$) tglmi = VAL(tglmi$) blnmi = VAL(blnmi$) thnmi = VAL(thnmi$) phdp = VAL(phdp$) tglval = 31 blnval = 12 thnval = 2005 IF blnval = 1 OR bulanval = 5 OR bulanval = 7 OR bulanval = 10 OR blnval = 12 THEN bulan = 30 IF blnval = 2 OR bulanval = 4 OR bulanval = 6 OR bulanval = 8 OR blnval = 9 OR blnval = 11 THEN bulan = 31 IF blnval = 3 AND (thnval / 4) - INT(thnval / 4) = 0 THEN bulan = 29 IF blnval = 3 AND (thnval / 4) - INT(thnval / 4) > 0 THEN bulan = 28 hrus = tglval - tgllhr blnus = blnval - blnlhr thnus = thnval - thnlhr IF hrus < 0 THEN hrus = hrus + bulan blnus = blnus - 1 END IF IF blnus < 0 THEN blnus = blnus + 12 thnus = thnus - 1 END IF IF hrus > 15 THEN
LAMPIRAN 3
42
blnus = blnus + 1 hrus = 0 END IF IF blnus >= 12 THEN thnus = thnus + 1 blnus = blnus - 12 END IF usia = thnus + blnus / 12 x = CINT(usia) LOCATE 3, 5: PRINT "BACA DATA PEGAWAI AKTIF" LOCATE 5, 5: PRINT "NOMOR :"; i LOCATE 6, 5: PRINT "NIK :"; NIK$ LOCATE 7, 5: PRINT USING "TGL LAHIR : ##-##-####"; tgllhr; blnlhr; thnlhr LOCATE 8, 5: PRINT USING "TGL PESERTA: ##-##-####"; tglmi; blnmi; thnmi LOCATE 9, 5: PRINT USING "PHDP : ##,###,###"; phdp LOCATE 10, 5: PRINT USING "SUSKEL : ###"; VAL(sts$) LOCATE 11, 5: PRINT USING "MK PENSIUN : ##-##"; VAL(LEFT$(mk$, 2)); VAL(RIGHT$(mk$, 3)) LOCATE 12, 5: PRINT USING "USIA : ## thn ## bln"; thnus; blnus LOCATE 13, 5: PRINT USING "ist - ank : ## - ##"; VAL(LEFT$(sts$, 2)) - 10; VAL(RIGHT$(sts$, 1)) ’INPUT b$ mk = VAL(LEFT$(mk$, 2)) + VAL(RIGHT$(mk$, 2)) / 12 ist = VAL(LEFT$(sts$, 2)) - 10 ank = VAL(RIGHT$(sts$, 1)) mk = 0 IF x >= 56 THEN peg0 = peg0 + 1 IF x < 56 THEN
LAMPIRAN 3
43
FOR th = 1 TO 1 MPN = .025 * (mk + 56 - x) * phdp IF MPN > .75 * phdp THEN MPN = .75 * phdp thn = th IF thn > 56 - x THEN thn = 56 - x MSDR = .025 * (mk + thn - 1) * phdp IF MSDR > .75 * phdp THEN MSDR = .75 * phdp MJND = .67 * MSDR IF MJND > .5 * phdp THEN MJND = .5 * phdp MYTM = MJND IF th <= 56 - x THEN ’*********************************** ’*** PERHITUNGAN NORMAL COST *** ’*********************************** FOR j = 1 TO 57 - x - th MPSDR = .025 * (mk + j + th - 1) * phdp IF MPSDR > .75 * phdp THEN MPSDR = .75 * phdp MPJND = .67 * MPSDR MPYTM = MPJND MPCCT = .025 * (56 - x + mk) * phdp IF MPSDR > .75 * phdp THEN MPSDR = .75 * phdp IF MPJND > .5 * phdp THEN MPJND = .5 * phdp PVPENCAT(th) = PVPENCAT(th) + MPCCT * (1 + skl) ^(j - th) * lx(x + th - 1 + j) / lx(x + th - 1) * qxc(x + th - 1 + j) * v ^j * ax(x + th - 1 + j) * 12 PVPENJND(th) = PVPENJND(th) + MPJND * (1 + skl) ^(j - th) * (lx(x + th - 1 + j) * lx(x + th - 1 + j - 3)) / (lx(x + th - 1) * lx(x + th - 1 - 3)) * (lx(x + th - 1 + j) - lx(x + th - 1 + j + 1)) / lx(x + th - 1 + j) * v ^j * ax(x + th - _ 1 + j - 3) * 12 * ist IF x + th - 1 + j - 30 > 25 GOTO dewasa IF x + th - 1 - 30 < 5 THEN x = 35 - th + 1
LAMPIRAN 3
44
PVPENYTM(th) = PVPENYTM(th) + MPYTM * (1 + skl) ^(j - th) * (lx(x + th - 1 + j) * lx(x + th - 1 + j - 30)) / (lx(x + th - 1) * lx(x + th - 1 - 30)) * (lx(x + th - 1 + j) - lx(x + th - 1 + j + 1)) / lx(x + th - 1 + j) * v ^j * (ax(x + _ th - 1 + j - 30) - ax(25)) * 12 * ank dewasa: IF mk + th - 1 + j > 3 AND x + th - 1 + j < 46 THEN PVPENTUNDA(th) = PVPENTUNDA(th) + MPSDR * (1 + skl) ^(j - th) * lx(x + th - 1 + j) / lx(x + th - 1) * qxw(x + th - 1 + j) * v ^j * lx(46) / lx(x + th - 1 + j) * v ^(46 - (x + th - 1) - j) * ax(46) * 12 END IF IF mk + th - 1 + j <= 3 AND x + th - 1 + j < 46 THEN IURPEG = .075 * phdp * (1 - (1 + bu / 12) ^(-(mk + th - 1 + j) * 12)) / (bu / 12) * (1 + bu / 12) PVPENNT(th) = PVPENNT(th) + IURPEG * lx(x + th - 1 + j) / lx(x + th - 1) * qxw(x + th - 1 + j) * v ^j END IF PVFP(th) = PVFP(th) + phdp * (1 + skl) ^(j - th) * 12 * lx(x + th - 1 + j) / lx(x + th - 1) * v ^(j - 1) NEXT j PVFBIAYA = PVFP * .05 FOR j = 1 TO 56 - 46 PVPENCPT(th) = PVPENCPT(th) + MPN * (1 + skl) ^(46 - (x + th - 1)) * lx(46) / lx(x + th - 1) * v ^(46 - (x + th - 1)) * qxw(46 + th - 1 + j) * v ^j * ax(46 + th - 1 + j) * 12 NEXT j PVPENS(th) = PVPENS(th) + MPN * (1 + skl) ^(56 - (x + th - 1)) * v ^(56 - (x + th - 1)) * lx(56) / lx(x + th - 1) * ax(56) * 12 END IF IF th > 56 - x THEN MPSDR = .025 * (mk + 56 - x) * phdp
LAMPIRAN 3
45
IF MPSDR > .75 * phdp THEN MPSDR = .75 * phdp MPJND = .67 * MPSDR MPYTM = MPJND MPCCT = .025 * (56 - x + mk) * phdp IF MPSDR > .75 * phdp THEN MPSDR = .75 * phdp IF MPJND > .5 * phdp THEN MPJND = .5 * phdp PEGPEN = lx(x + th) / lx(x) SENDIRI(th) = SENDIRI(th) + PEGPEN MANSDR(th) = MANSDR(th) + MPN * (1 + skl) ^(56 - x) * PEGPEN PEGMAT = lx(x + th - 1) / lx(x) * qxm(x + th - 1) MATI(th) = MATI(th) + PEGMAT PENJND = (lx(x + th - 1) * lx(x - 3 + th - 1)) / (lx(x) * lx(x - 3)) * qxm(x + th - 1) * ist JANDA(th) = JANDA(th) + PENJND MANJND(th) = MANJND(th) + MJND * (1 + skl) ^(th) * PENJND FOR j = 1 TO 99 - 56 - th PVPENJND(th) = PVPENJND(th) + MPJND * (1 + skl) ^(56 - x) * (lx(x + th - 1 + j) * lx(x + th - 1 + j - 3)) / (lx(x + th - 1) * lx(x + th - 1 - 3)) * (lx(x + th - 1 + j) - lx(x + th - 1 + j + 1)) / lx(x + th - 1 + j) * v ^j * ax(x + th - 1 +j_ - 3) * 12 * ist IF x + th - 1 + j - 30 > 25 GOTO dewasa1 IF x + th - 1 - 30 < 5 THEN x = 35 - th + 1 PVPENYTM(th) = PVPENYTM(th) + MPYTM * (1 + skl) ^(56 - x) * (lx(x + th - 1 + j) * lx(x + th - 1 + j - 30)) / (lx(x + th - 1) * lx(x + th - 1 - 30)) * (lx(x + th - 1 + j) - lx(x + th - 1 + j + 1)) / lx(x + th - 1 + j) * v ^j * (ax(x + th - 1 _ + j - 30) - ax(25)) * 12 * ank dewasa1: IF mk + 56 - x - 1 + j <= 3 AND x + 56 - x - 1 + j < 46 THEN
LAMPIRAN 3
46
IURPEG = .075 * phdp * (1 - (1 + bu / 12) ^(-(mk + th - 1 + j) * 12)) / (bu / 12) * (1 + bu / 12) PVPENNT(th) = PVPENNT(th) + IURPEG * lx(x + th - 1 + j) / lx(x + th - 1) * qxw(x + th - 1 + j) * v ^j END IF NEXT j PVPENS(th) = PVPENS(th) + MPN * (1 + skl) ^(56 - x) * v ^((x + th - 1) - 56) * lx(x + th - 1) / lx(56) * ax(x + th - 1) * 12 END IF PVFB(th) = PVPENCAT(th) + PVPENS(th) + PVPENJND(th) + PVPENYTM(th) + PVPENCPT(th) + PVPENTUNDA(th) + PVPENNT(th) ALAKTIF(th) = PVFB(th) - PVFP(th) LOCATE 15, 10: PRINT "PERHITUNGAN NORMAL COST" LOCATE 16, 10: PRINT "=======================" LOCATE 18, 10: PRINT USING "PVPENS : ###,###,###,###.##"; PVPENS(th) LOCATE 19, 10: PRINT USING "PVPENCAT : ###,###,###,###.##"; PVPENCAT(th) LOCATE 20, 10: PRINT USING "PVPENSJND : ###,###,###,###.##"; PVPENJND(th) LOCATE 21, 10: PRINT USING "PVPENSYTM : ###,###,###,###.##"; PVPENYTM(th) LOCATE 22, 10: PRINT USING "PVPENCEPAT: ###,###,###,###.##"; PVPENCPT(th) LOCATE 23, 10: PRINT USING "PVPENTUNDA: ###,###,###,###.##"; PVPENTUNDA(th) LOCATE 24, 10: PRINT USING "PVNILTUN : ###,###,###,###.##"; PVPENNT(th) LOCATE 25, 10: PRINT USING "PVFB (AKT): ###,###,###,###.##"; PVFB(th)
LAMPIRAN 3
47
LOCATE 26, 10: PRINT USING "PVF PHDP : ###,###,###,###.##"; PVFP(th) NEXT th END IF NEXT i NC = PVFB(0) / PVFP(0) LOCATE 28, 10: PRINT USING "NORMAL COST : ###,###.###"; NC INPUT b$ END
