Bowers, N., Gerber, H., Hickman, J.C., Jones, D.A., and Nesbitt, C. (1997) "Ac- tuarial Mathematics", 2nd ed., Schaumburg, IL: Society of Actuaries.
Howard E., Winklevoss, PhD., "Pension Mathematics With Numerical Illustra- tions", Associate Professor Of Insurance And Actuarial Science Wharton School.
Jordan Jr., Chester Walace, 1967, "Life Contingencies", The Society of Actu- aries.
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
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
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
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
LAMPIRAN 2 36 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
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
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), ALPEN- SIUNAN(100)
DIM PVSDRTUNDA(100), PVJNDTUNDA(100), PVYTMTUNDA(100), AL- TUNDA(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
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
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
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
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
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)
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
