Saran - KESIMPULAN DAN SARAN - EVALUASI PREMI POLIS JOINT LIFE PASANGAN SUAMI ISTRI MENGGUNAKAN

BAB V KESIMPULAN DAN SARAN

5.2 Saran

Pada penelitian ini dilakukan perhitungan dan perbandingan besar premi asuransi jiwa joint life pasangan suami istri dengan Copula Frank menggunakan suku bunga Vasicek, Langevin dan CIR dimana benefit dibayarkan di akhir tahun kematian peserta. Adapun saran yang dapat diberikan untuk peneliti selanjutnya yaitu dapat dilakukan perhitungan dan perbandingan besar premi asuransi jiwa joint life pasangan suami istri dengan Copula Clayton atau Copula Gumbel menggunakan suku bunga stokastik lainnya dimana benefit diberikan tepat saat peserta pertama meninggal dunia.

REFERENSI

[1] D. Lestari, N. Satyahadewi and H. Perdana, "Model Multiple Decrement dalam Penentuan Premi Asuransi Jiwa," Buletin Ilmiah Math.Stat. dan Terapannya (Bimaster), vol. 8, no. 3, pp. 463-470, 2019.

[2] M. A. Siregar, Mustafid and R. Santoso, "Pengukuran Probabilitas Kebangkitan Obligasi Korporasi dengan Suku Bunga Cox Ingersoll Ross Model Merton," Jurnal Gaussian , vol. 7, no. 2, pp. 175-186, 2018.

[3] I. M. W. Wiguna, K. Jayanegara and I. N. Widana, "Perhitungan Premi Asuransi Joint Life dengan Model Vasicek dan CIR," E-Journal Matematika , vol. 8, no. 3, pp. 246-252, 2019.

[4] P. Margus, "Generalized Frasier Claim Rates Under Survivorship Life Insurances Policies," North American Actuarial Jurnal , vol. 6, no. 2, pp. 76-94, 2002.

[5] I. Fauziah, "Evaluasi Premi Polis Last Survivor Pasangan Suami Istri Menggunakan Copula Frank," Jurnal CAUCHY, vol. 3, pp. 42-48, 2013.

[6] I. N. Widana and N. M. Asih, "Evaluasi Premi Joint Life Pasangan Suami Istri Menggunakan Copula Frank," Jurnal Matematika, vol. 8, no. 1, pp. 57-62, 2018.

[7] A. R. Effendie, Matematika Aktuaria dengan Software R, Yogyakarta:

Gadjah Mada University Press, 2015.

[8] R. J. Cunningham, T. N. Herzog and L. R. London, Models for Quantifying Risk Second Edition, United States: ACTEX Publication, 2006.

[9] N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones and C. J. Nesbitt, Actuarial Mathematics, The Society of Actuaries, 1997.

[10] T. Futami, Matematika Asuransi Jiwa II, Tokyo: Incorporated Foundation Oriental Life Insurance Cultural Development Center, 1994 .

[11] S. M. Ross, Stochastic Processes, Jhon Wiley & Sons, 1996.

[12] J. C. Hull, Option, Futures, and Other Derivatives,, United States of America : Prentice Hall, 2012.

[13] K. Khotimah, Mahmudi and N. Fitriyani, "Calculation and Management of Premium Funds in Sharia Insurance based on Langevin Type Modelof Return of Investment," Inprime, vol. 1, no. 2, pp. 128-135, 2019.

[14] R. B. Nelsen, An Intoduction to Copulas Second Edition, USA: Springer , 2006 .

[15] A. E. Shemyakin and H. Youn, "Copula Models of Joint Survival Analysis,"

Applied Stochastic Models in Business And Industry, vol. 22, pp. 211-224, 2006.

LAMPIRAN

Lampiran 1 : Tabel Mortalita Indonesia (TMI) Tahun 2011

(laki-laki) Px lx Y

(perempuan) Py ly

55 0.00961 0.99039 90884.2 55 0.00607 0.99393 94053.2 56 0.01051 0.98949 90010.8 56 0.00669 0.99331 93482.3 57 0.01142 0.98858 89064.8 57 0.00725 0.99275 92856.9 58 0.01232 0.98768 88047.7 58 0.00776 0.99224 92183.7 59 0.01322 0.98678 86962.9 59 0.00826 0.99174 91468.4 60 0.01417 0.98583 85813.3 60 0.00877 0.99123 90712.8 61 0.01521 0.98479 84597.3 61 0.00936 0.99064 89917.3 62 0.01639 0.98361 83310.6 62 0.01004 0.98996 89075.7 63 0.01773 0.98227 81945.1 63 0.01104 0.98896 88181.3 64 0.01926 0.98074 80492.2 64 0.01214 0.98786 87207.8 65 0.021 0.979 78942 65 0.01334 0.98666 86149.1 66 0.02288 0.97712 77284.2 66 0.01466 0.98534 84999.9 67 0.02486 0.97514 75515.9 67 0.01612 0.98388 83753.8 68 0.02702 0.97298 73638.6 68 0.01771 0.98229 82403.7 69 0.02921 0.97079 71648.9 69 0.01947 0.98053 80944.3 70 0.03182 0.96818 69556 70 0.02121 0.97879 79368.3 71 0.03473 0.96527 67342.7 71 0.02319 0.97681 77684.9 72 0.03861 0.96139 65003.9 72 0.02539 0.97461 75883.4 73 0.04264 0.95736 62494.1 73 0.02778 0.97222 73956.7 74 0.04687 0.95313 59829.4 74 0.03042 0.96958 71902.2 75 0.05155 0.94845 57025.2 75 0.0333 0.9667 69714.9 76 0.05664 0.94336 54085.5 76 0.03646 0.96354 67393.4 77 0.06254 0.93746 51022.1 77 0.03991 0.96009 64936.3 78 0.06942 0.93058 47831.2 78 0.04372 0.95628 62344.7 79 0.07734 0.92266 44510.8 79 0.04789 0.95211 59619 80 0.08597 0.91403 41068.3 80 0.05247 0.94753 56763.8

Lampiran 2: Data BI 7-Day Repo Rate Tanggal BI 7-Day Tanggal BI

7-Day 13-Oct-20 4.00% 19-Jul-18 5.25%

17-Sep-20 4.00% 29-Jun-18 5.25%

19-Aug-20 4.00% 30-May-18 4.75%

16-Jul-20 4.00% 17-May-18 4.50%

18-Jun-20 4.25% 19-Apr-18 4.25%

19-May-20 4.50% 22-Mar-18 4.25%

14-Apr-20 4.50% 15-Feb-18 4.25%

19-Mar-20 4.50% 18-Jan-18 4.25%

20-Feb-20 4.75% 14-Dec-17 4.25%

23-Jan-20 5.00% 16-Nov-17 4.25%

19-Dec-19 5.00% 19-Oct-17 4.25%

21-Nov-19 5.00% 22-Sep-17 4.25%

24-Oct-19 5.00% 22-Aug-17 4.50%

19-Sep-19 5.25% 20-Jul-17 4.75%

22-Aug-19 5.50% 15-Jun-17 4.75%

18-Jul-19 5.75% 18-May-17 4.75%

20-Jun-19 6.00% 20-Apr-17 4.75%

16-May-19 6.00% 16-Mar-17 4.75%

25-Apr-19 6.00% 16-Feb-17 4.75%

21-Mar-19 6.00% 19-Jan-17 4.75%

21-Feb-19 6.00% 15-Dec-16 4.75%

17-Jan-19 6.00% 17-Nov-16 4.75%

20-Dec-18 6.00% 20-Oct-16 4.75%

15-Nov-18 6.00% 22-Sep-16 5.00%

23-Oct-18 5.75% 19-Aug-16 5.25%

27-Sep-18 5.75% 21-Jul-16 5.25%

15-Aug-18 5.50% 16-Jun-16 5.25%

19-Jul-18 5.25% 19-May-16 5.50%

29-Jun-18 5.25% 21-Apr-16 5.50%

Lampiran 3 : Suku Bunga Stokastik pertahun untuk setiap variasi 𝑟(0) Tahun

Lampiran 4 : Nilai premi tunggal, anuitas dan premi tahunan untuk suku bunga Vasicek (untuk 𝑟(0) = 4.5% dan 4.75%) Usia

Suami

Usia Istri

alpha = -3.367 dan r(0)=4.5% alpha=-3.367 dan r(0)=4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,408,725 7.191628 Rp 2,420,693 Rp 17,371,718 7.178951 Rp 2,419,813 61 56 Rp 18,609,660 7.140964 Rp 2,606,043 Rp 18,570,133 7.128401 Rp 2,605,091 62 57 Rp 19,897,928 7.086706 Rp 2,807,782 Rp 19,855,694 7.074266 Rp 2,806,750 63 58 Rp 21,308,821 7.028155 Rp 3,031,922 Rp 21,263,614 7.015847 Rp 3,030,798 64 59 Rp 22,841,410 6.964363 Rp 3,279,756 Rp 22,792,977 6.952199 Rp 3,278,528 65 60 Rp 24,491,513 6.894751 Rp 3,552,197 Rp 24,439,614 6.882744 Rp 3,550,854 66 61 Rp 26,256,657 6.818926 Rp 3,850,556 Rp 26,201,060 6.80709 Rp 3,849,084 67 62 Rp 28,140,945 6.73633 Rp 4,177,489 Rp 28,081,413 6.72468 Rp 4,175,873 68 63 Rp 30,162,234 6.646024 Rp 4,538,387 Rp 30,098,509 6.634578 Rp 4,536,613 69 64 Rp 32,323,917 6.548446 Rp 4,936,120 Rp 32,255,714 6.537219 Rp 4,934,164 70 65 Rp 34,647,759 6.441761 Rp 5,378,616 Rp 34,574,779 6.430774 Rp 5,376,457 Usia

Suami

Usia Istri

alpha=-3 dan r(0)=4.5% alpha=-3 dan r(0)=4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,572,310 7.186713 Rp 2,445,111 Rp 17,534,930 7.174048 Rp 2,444,217 61 56 Rp 18,790,075 7.13547 Rp 2,633,334 Rp 18,750,137 7.12292 Rp 2,632,366 62 57 Rp 20,096,347 7.080584 Rp 2,838,233 Rp 20,053,661 7.068158 Rp 2,837,183 63 58 Rp 21,526,700 7.021341 Rp 3,065,896 Rp 21,480,998 7.009049 Rp 3,064,752 64 59 Rp 23,080,196 6.956775 Rp 3,317,657 Rp 23,031,220 6.944629 Rp 3,316,408 65 60 Rp 24,752,569 6.886294 Rp 3,594,469 Rp 24,700,078 6.874306 Rp 3,593,101 66 61 Rp 26,540,947 6.809494 Rp 3,897,639 Rp 26,484,707 6.79768 Rp 3,896,139 67 62 Rp 28,449,187 6.725814 Rp 4,229,850 Rp 28,388,959 6.714189 Rp 4,228,204

68 63 Rp 30,494,774 6.634315 Rp 4,596,522 Rp 30,430,302 6.622895 Rp 4,594,713 69 64 Rp 32,680,104 6.535464 Rp 5,000,426 Rp 32,611,103 6.524267 Rp 4,998,432 70 65 Rp 35,026,254 6.427433 Rp 5,449,494 Rp 34,952,430 6.416478 Rp 5,447,292 Usia

Suami

Usia Istri

alpha=-2.5 dan r(0)=4.5% alpha=-2.5 dan r(0)=4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,801,795 7.179941 Rp 2,479,379 Rp 17,763,890 7.167291 Rp 2,478,466 61 56 Rp 19,044,044 7.127878 Rp 2,671,769 Rp 19,003,526 7.115346 Rp 2,670,780 62 57 Rp 20,376,670 7.0721 Rp 2,881,276 Rp 20,333,344 7.059694 Rp 2,880,202 63 58 Rp 21,835,702 7.01187 Rp 3,114,106 Rp 21,789,295 6.999599 Rp 3,112,935 64 59 Rp 23,420,213 6.946195 Rp 3,371,661 Rp 23,370,463 6.934073 Rp 3,370,380 65 60 Rp 25,125,836 6.874463 Rp 3,654,952 Rp 25,072,496 6.862503 Rp 3,653,550 66 61 Rp 26,949,146 6.796254 Rp 3,965,294 Rp 26,891,980 6.78447 Rp 3,963,755 67 62 Rp 28,893,656 6.711 Rp 4,305,417 Rp 28,832,423 6.699409 Rp 4,303,727 68 63 Rp 30,976,346 6.617758 Rp 4,680,791 Rp 30,910,788 6.606377 Rp 4,678,932 69 64 Rp 33,198,193 6.517041 Rp 5,094,059 Rp 33,128,027 6.505886 Rp 5,092,008 70 65 Rp 35,579,284 6.407022 Rp 5,553,171 Rp 35,504,223 6.396114 Rp 5,550,905 Usia

Suami

Usia Istri

alpha=-2 dan r(0)=4.5% alpha=-2 dan r(0)=4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 18,036,179 7.173164 Rp 2,514,396 Rp 17,997,736 7.160531 Rp 2,513,464 61 56 Rp 19,304,491 7.120259 Rp 2,711,206 Rp 19,263,376 7.107744 Rp 2,710,195 62 57 Rp 20,665,363 7.063556 Rp 2,925,631 Rp 20,621,377 7.05117 Rp 2,924,533 63 58 Rp 22,155,372 7.002298 Rp 3,164,015 Rp 22,108,235 6.99005 Rp 3,162,815 64 59 Rp 23,773,637 6.935463 Rp 3,427,837 Rp 23,723,081 6.923366 Rp 3,426,524 65 60 Rp 25,515,707 6.862415 Rp 3,718,182 Rp 25,461,479 6.850483 Rp 3,716,742 66 61 Rp 27,377,610 6.782716 Rp 4,036,379 Rp 27,319,469 6.770963 Rp 4,034,798

67 62 Rp 29,362,514 6.69579 Rp 4,385,220 Rp 29,300,217 6.684234 Rp 4,383,482 68 63 Rp 31,486,894 6.600687 Rp 4,770,245 Rp 31,420,180 6.589345 Rp 4,768,331 69 64 Rp 33,750,261 6.497961 Rp 5,193,977 Rp 33,678,850 6.486851 Rp 5,191,864 70 65 Rp 36,171,658 6.385788 Rp 5,664,400 Rp 36,095,266 6.37493 Rp 5,662,065 Usia

Suami

Usia Istri

alpha=-1.5 dan r(0)=4.5% alpha=-1.5 dan r(0)=4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 18,271,618 7.166498 Rp 2,549,588 Rp 18,232,635 7.15388 Rp 2,548,636 61 56 Rp 19,567,211 7.112739 Rp 2,751,009 Rp 19,525,494 7.100242 Rp 2,749,976 62 57 Rp 20,957,858 7.055096 Rp 2,970,599 Rp 20,913,202 7.042729 Rp 2,969,474 63 58 Rp 22,480,773 6.992785 Rp 3,214,853 Rp 22,432,891 6.980559 Rp 3,213,624 64 59 Rp 24,135,162 6.924755 Rp 3,485,345 Rp 24,083,780 6.912683 Rp 3,483,999 65 60 Rp 25,916,527 6.850346 Rp 3,783,243 Rp 25,861,384 6.838442 Rp 3,781,765 66 61 Rp 27,820,365 6.769096 Rp 4,109,908 Rp 27,761,214 6.757376 Rp 4,108,283 67 62 Rp 29,849,511 6.680422 Rp 4,468,208 Rp 29,786,105 6.668901 Rp 4,466,419 68 63 Rp 32,019,954 6.583362 Rp 4,863,769 Rp 31,952,030 6.57206 Rp 4,861,798 69 64 Rp 34,329,703 6.47851 Rp 5,299,012 Rp 34,256,981 6.467445 Rp 5,296,834 70 65 Rp 36,796,716 6.36404 Rp 5,781,975 Rp 36,718,915 6.353232 Rp 5,779,565 Usia

Suami

Usia Istri

alpha=-1 dan r(0)=4.5% alpha=-1 dan r(0)=4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 18,503,517 7.160071 Rp 2,584,264 Rp 18,464,001 7.147468 Rp 2,583,293 61 56 Rp 19,827,117 7.105465 Rp 2,790,404 Rp 19,784,803 7.092985 Rp 2,789,348 62 57 Rp 21,248,552 7.046882 Rp 3,015,312 Rp 21,203,228 7.034535 Rp 3,014,162 63 58 Rp 22,805,759 6.983515 Rp 3,265,656 Rp 22,757,132 6.97131 Rp 3,264,398 64 59 Rp 24,498,089 6.914279 Rp 3,543,116 Rp 24,445,875 6.902231 Rp 3,541,735 65 60 Rp 26,321,039 6.838488 Rp 3,848,956 Rp 26,264,969 6.826611 Rp 3,847,439

66 61 Rp 28,269,614 6.755656 Rp 4,184,585 Rp 28,209,436 6.743966 Rp 4,182,915 67 62 Rp 30,346,346 6.665186 Rp 4,552,963 Rp 30,281,806 6.6537 Rp 4,551,123 68 63 Rp 32,566,770 6.566105 Rp 4,959,831 Rp 32,497,601 6.554843 Rp 4,957,800 69 64 Rp 34,927,391 6.459042 Rp 5,407,518 Rp 34,853,312 6.448022 Rp 5,405,272 70 65 Rp 37,445,052 6.342166 Rp 5,904,142 Rp 37,365,783 6.331409 Rp 5,901,654 Usia

Suami

Usia Istri

alpha=1 dan r(0)=4.5% alpha=1 dan r(0)=4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 19,299,448 7.139153 Rp 2,703,325 Rp 19,258,095 7.126599 Rp 2,702,284 61 56 Rp 20,729,577 7.081588 Rp 2,927,250 Rp 20,685,182 7.069164 Rp 2,926,114 62 57 Rp 22,270,389 7.019677 Rp 3,172,566 Rp 22,222,711 7.007393 Rp 3,171,323 63 58 Rp 23,963,400 6.95251 Rp 3,446,726 Rp 23,912,105 6.940378 Rp 3,445,360 64 59 Rp 25,809,231 6.878872 Rp 3,751,957 Rp 25,753,997 6.866907 Rp 3,750,451 65 60 Rp 27,804,111 6.797959 Rp 4,090,068 Rp 27,744,627 6.786176 Rp 4,088,404 66 61 Rp 29,941,946 6.709169 Rp 4,462,839 Rp 29,877,921 6.697588 Rp 4,460,997 67 62 Rp 32,224,771 6.61183 Rp 4,873,805 Rp 32,155,916 6.600469 Rp 4,871,762 68 63 Rp 34,667,139 6.504888 Rp 5,329,398 Rp 34,593,153 6.493769 Rp 5,327,130 69 64 Rp 37,260,251 6.389055 Rp 5,831,887 Rp 37,180,832 6.378198 Rp 5,829,363 70 65 Rp 40,016,761 6.262439 Rp 6,389,965 Rp 39,931,621 6.251866 Rp 6,387,152

Lampiran 5: Nilai Premi Tunggal, Anuitas, dan Premi Tahunan untuk suku bunga Vasicek (untuk 𝑟(0) = 5% dan 5. 55%) Usia

Suami

Usia Istri

alpha=-3.367 dan r(0)=5% alpha=-3.367 dan r(0)=5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,334,824 7.166313 Rp 2,418,932 Rp 17,254,051 7.138641 Rp 2,416,994 61 56 Rp 18,530,727 7.115877 Rp 2,604,138 Rp 18,444,454 7.088454 Rp 2,602,042 62 57 Rp 19,813,588 7.061863 Rp 2,805,717 Rp 19,721,404 7.034708 Rp 2,803,443 63 58 Rp 21,218,544 7.003576 Rp 3,029,673 Rp 21,119,872 6.976709 Rp 3,027,197 64 59 Rp 22,744,690 6.940071 Rp 3,277,299 Rp 22,638,976 6.913518 Rp 3,274,596 65 60 Rp 24,387,872 6.870772 Rp 3,549,510 Rp 24,274,593 6.844562 Rp 3,546,552 66 61 Rp 26,145,632 6.795289 Rp 3,847,611 Rp 26,024,280 6.769451 Rp 3,844,371 67 62 Rp 28,022,062 6.713065 Rp 4,174,258 Rp 27,892,122 6.687633 Rp 4,170,701 68 63 Rp 30,034,978 6.623165 Rp 4,534,838 Rp 29,895,885 6.598177 Rp 4,530,931 69 64 Rp 32,187,717 6.526026 Rp 4,932,208 Rp 32,038,847 6.501517 Rp 4,927,903 70 65 Rp 34,502,019 6.419819 Rp 5,374,298 Rp 34,342,722 6.395833 Rp 5,369,546 Usia

Suami

Usia Istri

alpha=-3 dan r(0)=5% alpha=-3 dan r(0)=5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,497,663 7.161421 Rp 2,443,323 Rp 17,416,074 7.133775 Rp 2,441,355 61 56 Rp 18,710,320 7.110409 Rp 2,631,399 Rp 18,623,149 7.083014 Rp 2,629,269 62 57 Rp 20,011,105 7.05577 Rp 2,836,133 Rp 19,917,934 7.028645 Rp 2,833,823 63 58 Rp 21,435,434 6.996794 Rp 3,063,608 Rp 21,335,680 6.969961 Rp 3,061,090 64 59 Rp 22,982,394 6.932519 Rp 3,315,158 Rp 22,875,495 6.906004 Rp 3,312,407 65 60 Rp 24,647,747 6.862355 Rp 3,591,733 Rp 24,533,175 6.836187 Rp 3,588,722 66 61 Rp 26,428,637 6.785901 Rp 3,894,639 Rp 26,305,882 6.760111 Rp 3,891,339 67 62 Rp 28,328,915 6.702598 Rp 4,226,557 Rp 28,197,457 6.677219 Rp 4,222,934 68 63 Rp 30,366,025 6.611509 Rp 4,592,904 Rp 30,225,300 6.58658 Rp 4,588,922

69 64 Rp 32,542,311 6.513103 Rp 4,996,437 Rp 32,391,701 6.48866 Rp 4,992,048 70 65 Rp 34,878,830 6.405556 Rp 5,445,090 Rp 34,717,693 6.381643 Rp 5,440,244 Usia

Suami

Usia Istri

alpha=-2.5 dan r(0)=5% alpha=-2.5 dan r(0)=5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,726,100 7.15468 Rp 2,477,553 Rp 17,643,366 7.127068 Rp 2,475,544 61 56 Rp 18,963,131 7.102852 Rp 2,669,791 Rp 18,874,694 7.075496 Rp 2,667,614 62 57 Rp 20,290,150 7.047325 Rp 2,879,128 Rp 20,195,584 7.020244 Rp 2,876,764 63 58 Rp 21,743,029 6.987366 Rp 3,111,763 Rp 21,641,739 6.960581 Rp 3,109,186 64 59 Rp 23,320,865 6.921987 Rp 3,369,100 Rp 23,212,278 6.895526 Rp 3,366,281 65 60 Rp 25,019,319 6.850579 Rp 3,652,147 Rp 24,902,896 6.82447 Rp 3,649,059 66 61 Rp 26,834,987 6.772722 Rp 3,962,216 Rp 26,710,211 6.746998 Rp 3,958,829 67 62 Rp 28,771,376 6.687852 Rp 4,302,035 Rp 28,637,724 6.662548 Rp 4,298,314 68 63 Rp 30,845,428 6.595029 Rp 4,677,072 Rp 30,702,333 6.570184 Rp 4,672,979 69 64 Rp 33,058,075 6.494765 Rp 5,089,957 Rp 32,904,924 6.470414 Rp 5,085,443 70 65 Rp 35,429,390 6.385239 Rp 5,548,639 Rp 35,265,553 6.361428 Rp 5,543,653 Usia

Suami

Usia Istri

alpha=-2 dan r(0)=5% alpha=-2 dan r(0)=5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,959,411 7.147935 Rp 2,512,531 Rp 17,875,505 7.120357 Rp 2,510,479 61 56 Rp 19,222,387 7.095268 Rp 2,709,184 Rp 19,132,649 7.06795 Rp 2,706,959 62 57 Rp 20,577,525 7.038821 Rp 2,923,433 Rp 20,481,518 7.011783 Rp 2,921,014 63 58 Rp 22,061,242 6.977839 Rp 3,161,615 Rp 21,958,358 6.951102 Rp 3,158,975 64 59 Rp 23,672,679 6.911305 Rp 3,425,211 Rp 23,562,332 6.884898 Rp 3,422,321 65 60 Rp 25,407,416 6.838587 Rp 3,715,302 Rp 25,289,055 6.812539 Rp 3,712,133 66 61 Rp 27,261,505 6.759246 Rp 4,033,217 Rp 27,134,602 6.733591 Rp 4,029,737 67 62 Rp 29,238,109 6.672712 Rp 4,381,743 Rp 29,102,134 6.647485 Rp 4,377,916

68 63 Rp 31,353,669 6.578037 Rp 4,766,417 Rp 31,208,053 6.553278 Rp 4,762,205 69 64 Rp 33,607,656 6.475773 Rp 5,189,752 Rp 33,451,788 6.451519 Rp 5,185,103 70 65 Rp 36,019,106 6.364104 Rp 5,659,730 Rp 35,852,366 6.3404 Rp 5,654,591 Usia

Suami

Usia Istri

alpha=-1.5 dan r(0)=5% alpha=-1.5 dan r(0)=5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 18,193,771 7.1413 Rp 2,547,683 Rp 18,108,685 7.113756 Rp 2,545,587 61 56 Rp 19,483,904 7.087783 Rp 2,748,942 Rp 19,392,851 7.060504 Rp 2,746,667 62 57 Rp 20,868,682 7.0304 Rp 2,968,349 Rp 20,771,213 7.003404 Rp 2,965,874 63 58 Rp 22,385,155 6.96837 Rp 3,212,395 Rp 22,280,646 6.941682 Rp 3,209,690 64 59 Rp 24,032,553 6.900647 Rp 3,482,652 Rp 23,920,402 6.874294 Rp 3,479,689 65 60 Rp 25,806,408 6.826574 Rp 3,780,287 Rp 25,686,049 6.800587 Rp 3,777,034 66 61 Rp 27,702,243 6.74569 Rp 4,106,658 Rp 27,573,137 6.720104 Rp 4,103,082 67 62 Rp 29,722,892 6.657415 Rp 4,464,630 Rp 29,584,498 6.632266 Rp 4,460,692 68 63 Rp 31,884,312 6.560792 Rp 4,859,827 Rp 31,736,055 6.53612 Rp 4,855,488 69 64 Rp 34,184,480 6.456412 Rp 5,294,656 Rp 34,025,750 6.432256 Rp 5,289,862 70 65 Rp 36,641,351 6.342456 Rp 5,777,155 Rp 36,471,534 6.318862 Rp 5,771,852 Usia

Suami

Usia Istri

alpha=-1 dan r(0)=5% alpha=-1 dan r(0)=5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 18,424,605 7.134903 Rp 2,582,320 Rp 18,338,356 7.107391 Rp 2,580,181 61 56 Rp 19,742,618 7.080542 Rp 2,788,292 Rp 19,650,262 7.0533 Rp 2,785,967 62 57 Rp 21,158,043 7.022224 Rp 3,013,012 Rp 21,059,118 6.995271 Rp 3,010,479 63 58 Rp 22,708,653 6.959143 Rp 3,263,139 Rp 22,602,517 6.932501 Rp 3,260,370 64 59 Rp 24,393,819 6.890219 Rp 3,540,355 Rp 24,279,853 6.863919 Rp 3,537,316 65 60 Rp 26,209,070 6.81477 Rp 3,845,921 Rp 26,086,690 6.788844 Rp 3,842,582 66 61 Rp 28,149,441 6.732312 Rp 4,181,245 Rp 28,018,093 6.706794 Rp 4,177,569

67 62 Rp 30,217,463 6.642249 Rp 4,549,282 Rp 30,076,594 6.617178 Rp 4,545,230 68 63 Rp 32,428,642 6.543615 Rp 4,955,768 Rp 32,277,667 6.519031 Rp 4,951,298 69 64 Rp 34,779,457 6.437034 Rp 5,403,025 Rp 34,617,765 6.412977 Rp 5,398,080 70 65 Rp 37,286,756 6.320683 Rp 5,899,165 Rp 37,113,737 6.297199 Rp 5,893,689 Usia

Suami

Usia Istri

alpha=1 dan r(0)=5% alpha=1 dan r(0)=5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 19,216,869 7.114082 Rp 2,701,244 Rp 19,126,612 7.086677 Rp 2,698,954 61 56 Rp 20,640,923 7.056777 Rp 2,924,979 Rp 20,544,025 7.029656 Rp 2,922,480 62 57 Rp 22,175,177 6.995146 Rp 3,170,081 Rp 22,071,113 6.96833 Rp 3,167,346 63 58 Rp 23,860,967 6.928283 Rp 3,443,995 Rp 23,749,010 6.901799 Rp 3,440,988 64 59 Rp 25,698,931 6.854977 Rp 3,748,945 Rp 25,578,375 6.828857 Rp 3,745,630 65 60 Rp 27,685,325 6.774429 Rp 4,086,739 Rp 27,555,495 6.748709 Rp 4,083,077 66 61 Rp 29,814,092 6.686041 Rp 4,459,155 Rp 29,674,350 6.66076 Rp 4,455,100 67 62 Rp 32,087,270 6.589142 Rp 4,869,719 Rp 31,936,985 6.564341 Rp 4,865,223 68 63 Rp 34,519,392 6.482682 Rp 5,324,862 Rp 34,357,906 6.458409 Rp 5,319,872 69 64 Rp 37,101,654 6.367372 Rp 5,826,839 Rp 36,928,310 6.343669 Rp 5,821,285 70 65 Rp 39,846,740 6.241325 Rp 6,384,340 Rp 39,660,907 6.218245 Rp 6,378,151

Lampiran 6: Nilai Premi Tunggal, Anuitas, dan Premi Tahunan untuk suku bunga Vasicek (untuk 𝑟(0) = 6%) Usia

Suami

Usia Istri

alpha=-3.367 dan r(0)=6% alpha=-1.5 dan r(0)=6%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,188,364 7.116136 Rp 2,415,407 Rp 18,039,491 7.091354 Rp 2,543,871 61 56 Rp 18,374,293 7.066152 Rp 2,600,325 Rp 19,318,804 7.038317 Rp 2,744,804 62 57 Rp 19,646,437 7.012622 Rp 2,801,582 Rp 20,691,949 6.981449 Rp 2,963,847 63 58 Rp 21,039,629 6.954858 Rp 3,025,170 Rp 22,195,656 6.919976 Rp 3,207,476 64 59 Rp 22,553,005 6.891922 Rp 3,272,383 Rp 23,829,198 6.852861 Rp 3,477,263 65 60 Rp 24,182,470 6.823244 Rp 3,544,131 Rp 25,588,170 6.779453 Rp 3,774,371 66 61 Rp 25,925,593 6.748437 Rp 3,841,718 Rp 27,468,144 6.699295 Rp 4,100,154 67 62 Rp 27,786,450 6.66695 Rp 4,167,791 Rp 29,471,952 6.611812 Rp 4,457,470 68 63 Rp 29,782,770 6.577854 Rp 4,527,734 Rp 31,615,487 6.516054 Rp 4,851,937 69 64 Rp 31,917,781 6.481583 Rp 4,924,380 Rp 33,896,665 6.412609 Rp 5,285,939 70 65 Rp 34,213,175 6.376325 Rp 5,365,658 Rp 36,333,433 6.299672 Rp 5,767,512 Usia

Suami

Usia Istri

alpha=-3 dan r(0)=6% alpha=-1 dan r(0)=6%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,349,724 7.11129 Rp 2,439,744 Rp 18,268,216 7.085016 Rp 2,578,430 61 56 Rp 18,552,258 7.060734 Rp 2,627,525 Rp 19,575,157 7.031143 Rp 2,784,064 62 57 Rp 19,842,166 7.006585 Rp 2,831,931 Rp 20,978,671 6.973349 Rp 3,008,407 63 58 Rp 21,254,557 6.948138 Rp 3,059,029 Rp 22,516,204 6.910834 Rp 3,258,102 64 59 Rp 22,788,562 6.884439 Rp 3,310,155 Rp 24,187,173 6.84253 Rp 3,534,829 65 60 Rp 24,440,002 6.814904 Rp 3,586,258 Rp 25,987,167 6.767758 Rp 3,839,849 66 61 Rp 26,206,054 6.739135 Rp 3,888,637 Rp 27,911,277 6.68604 Rp 4,174,560 67 62 Rp 28,090,551 6.656579 Rp 4,219,968 Rp 29,962,035 6.596786 Rp 4,541,914 68 63 Rp 30,110,858 6.566305 Rp 4,585,662 Rp 32,154,890 6.499036 Rp 4,947,640

69 64 Rp 32,269,219 6.46878 Rp 4,988,455 Rp 34,486,272 6.39341 Rp 5,394,034 70 65 Rp 34,586,649 6.362193 Rp 5,436,278 Rp 36,973,032 6.278099 Rp 5,889,208 Usia

Suami

Usia Istri

alpha=-2.5 dan r(0)=6% alpha=1 dan r(0)=6%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,576,084 7.104611 Rp 2,473,898 Rp 19,053,213 7.064388 Rp 2,697,079 61 56 Rp 18,802,774 7.053247 Rp 2,665,832 Rp 20,465,227 7.007598 Rp 2,920,434 62 57 Rp 20,118,680 6.998218 Rp 2,874,829 Rp 21,986,486 6.946521 Rp 3,165,107 63 58 Rp 21,559,366 6.938797 Rp 3,107,075 Rp 23,657,965 6.88026 Rp 3,438,528 64 59 Rp 23,123,971 6.874005 Rp 3,363,974 Rp 25,480,336 6.807614 Rp 3,742,917 65 60 Rp 24,808,218 6.803236 Rp 3,646,532 Rp 27,449,914 6.72779 Rp 4,080,079 66 61 Rp 26,608,739 6.726077 Rp 3,956,056 Rp 29,560,710 6.640198 Rp 4,451,782 67 62 Rp 28,529,033 6.641969 Rp 4,295,268 Rp 31,814,770 6.54417 Rp 4,861,544 68 63 Rp 30,585,964 6.549977 Rp 4,669,629 Rp 34,226,581 6.438666 Rp 5,315,787 69 64 Rp 32,780,376 6.45061 Rp 5,081,749 Rp 36,787,342 6.324391 Rp 5,816,740 70 65 Rp 35,132,314 6.342062 Rp 5,539,573 Rp 39,509,783 6.199474 Rp 6,373,087 Usia

Suami

Usia Istri

alpha=-2 dan r(0)=6%

Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 17,807,270 7.097928 Rp 2,508,798 61 56 Rp 19,059,671 7.045733 Rp 2,705,137 62 57 Rp 20,403,443 6.989793 Rp 2,919,034 63 58 Rp 21,874,690 6.929358 Rp 3,156,813 64 59 Rp 23,472,595 6.863421 Rp 3,419,956 65 60 Rp 25,192,800 6.791355 Rp 3,709,540 66 61 Rp 27,031,401 6.712726 Rp 4,026,889 67 62 Rp 28,991,554 6.626968 Rp 4,374,784

68 63 Rp 31,089,633 6.533141 Rp 4,758,758 69 64 Rp 33,325,031 6.431793 Rp 5,181,297 70 65 Rp 35,716,766 6.321121 Rp 5,650,385

Lampiran 7: Nilai Premi Tunggal, Anuitas, dan Premi Tahunan untuk suku bunga Langevin (untuk 𝑟(0) = 4.5% 𝑑𝑎𝑛 4.75%) Usia

Suami

Usia Istri

alpha = -3.367 dan r(0) = 4.5% alpha = -3.367 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,316,591 6.285886 Rp 2,277,577 Rp 14,287,541 6.275554 Rp 2,276,698 61 56 Rp 15,313,081 6.245557 Rp 2,451,836 Rp 15,282,038 6.235312 Rp 2,450,886 62 57 Rp 16,381,535 6.202386 Rp 2,641,166 Rp 16,348,350 6.192236 Rp 2,640,137 63 58 Rp 17,548,285 6.1558 Rp 2,850,691 Rp 17,512,756 6.145751 Rp 2,849,571 64 59 Rp 18,816,390 6.105046 Rp 3,082,104 Rp 18,778,314 6.095107 Rp 3,080,883 65 60 Rp 20,185,358 6.049662 Rp 3,336,609 Rp 20,144,540 6.039843 Rp 3,335,276 66 61 Rp 21,655,129 5.989322 Rp 3,615,623 Rp 21,611,374 5.979634 Rp 3,614,163 67 62 Rp 23,231,036 5.923544 Rp 3,921,813 Rp 23,184,141 5.913999 Rp 3,920,214 68 63 Rp 24,929,272 5.851495 Rp 4,260,325 Rp 24,879,018 5.842106 Rp 4,258,570 69 64 Rp 26,750,072 5.773568 Rp 4,633,196 Rp 26,696,219 5.764348 Rp 4,631,264 70 65 Rp 28,715,867 5.688168 Rp 5,048,351 Rp 28,658,160 5.679132 Rp 5,046,222 Usia

Suami

Usia Istri

alpha = -3 dan r(0) = 4.5% alpha = -3 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,443,499 6.282111 Rp 2,299,147 Rp 14,414,169 6.271788 Rp 2,298,255 61 56 Rp 15,453,354 6.241332 Rp 2,475,970 Rp 15,422,002 6.231098 Rp 2,475,006 62 57 Rp 16,536,135 6.197675 Rp 2,668,119 Rp 16,502,610 6.187535 Rp 2,667,073 63 58 Rp 17,718,421 6.150552 Rp 2,880,786 Rp 17,682,519 6.140514 Rp 2,879,648 64 59 Rp 19,003,337 6.099197 Rp 3,115,711 Rp 18,964,852 6.089271 Rp 3,114,470 65 60 Rp 20,390,392 6.043136 Rp 3,374,141 Rp 20,349,126 6.033332 Rp 3,372,784 66 61 Rp 21,879,312 5.982035 Rp 3,657,503 Rp 21,835,069 5.972364 Rp 3,656,018 67 62 Rp 23,475,287 5.915408 Rp 3,968,498 Rp 23,427,862 5.905881 Rp 3,966,870 68 63 Rp 25,194,283 5.842417 Rp 4,312,305 Rp 25,143,456 5.833048 Rp 4,310,517

69 64 Rp 27,035,752 5.763482 Rp 4,690,871 Rp 26,981,283 5.754285 Rp 4,688,903 70 65 Rp 29,021,663 5.67701 Rp 5,112,139 Rp 28,963,300 5.667999 Rp 5,109,969 Usia

Suami

Usia Istri

alpha = -2.5 dan r(0) = 4.5% alpha = -2.5 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,621,036 6.276915 Rp 2,329,335 Rp 14,591,315 6.266603 Rp 2,328,425 61 56 Rp 15,650,233 6.235502 Rp 2,509,859 Rp 15,618,448 6.22528 Rp 2,508,875 62 57 Rp 16,753,871 6.191154 Rp 2,706,098 Rp 16,719,867 6.181029 Rp 2,705,030 63 58 Rp 17,958,919 6.143267 Rp 2,923,350 Rp 17,922,488 6.133245 Rp 2,922,187 64 59 Rp 19,268,612 6.091053 Rp 3,163,429 Rp 19,229,545 6.081145 Rp 3,162,159 65 60 Rp 20,682,477 6.034021 Rp 3,427,644 Rp 20,640,572 6.024237 Rp 3,426,255 66 61 Rp 22,199,951 5.971822 Rp 3,717,450 Rp 22,155,007 5.962173 Rp 3,715,928 67 62 Rp 23,826,031 5.903964 Rp 4,035,599 Rp 23,777,841 5.894462 Rp 4,033,929 68 63 Rp 25,576,381 5.829604 Rp 4,387,327 Rp 25,524,723 5.820264 Rp 4,385,492 69 64 Rp 27,449,349 5.749196 Rp 4,774,468 Rp 27,393,985 5.74003 Rp 4,772,447 70 65 Rp 29,466,251 5.661145 Rp 5,204,999 Rp 29,406,932 5.652169 Rp 5,202,769 Usia

Suami

Usia Istri

alpha = -2 dan r(0) = 4.5% alpha = -2 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,801,787 6.271723 Rp 2,360,083 Rp 14,771,666 6.261422 Rp 2,359,155 61 56 Rp 15,851,455 6.229658 Rp 2,544,514 Rp 15,819,226 6.21945 Rp 2,543,509 62 57 Rp 16,977,315 6.184597 Rp 2,745,096 Rp 16,942,818 6.174486 Rp 2,744,005 63 58 Rp 18,206,789 6.135916 Rp 2,967,249 Rp 18,169,812 6.125911 Rp 2,966,059 64 59 Rp 19,543,254 6.082805 Rp 3,212,869 Rp 19,503,583 6.072915 Rp 3,211,569 65 60 Rp 20,986,279 6.024754 Rp 3,483,342 Rp 20,943,707 6.014991 Rp 3,481,918 66 61 Rp 22,535,018 5.961398 Rp 3,780,157 Rp 22,489,339 5.951772 Rp 3,778,595 67 62 Rp 24,194,287 5.892236 Rp 4,106,130 Rp 24,145,292 5.882761 Rp 4,104,415

68 63 Rp 25,979,460 5.816419 Rp 4,466,573 Rp 25,926,924 5.807108 Rp 4,464,688 69 64 Rp 27,887,755 5.73443 Rp 4,863,213 Rp 27,831,439 5.725298 Rp 4,861,134 70 65 Rp 29,939,810 5.644676 Rp 5,304,080 Rp 29,879,467 5.635737 Rp 5,301,785 Usia

Suami

Usia Istri

alpha = -1.5 dan r(0) = 4.5% alpha = -1.5 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,982,779 6.266621 Rp 2,390,886 Rp 14,952,257 6.256333 Rp 2,389,940 61 56 Rp 16,053,756 6.223899 Rp 2,579,373 Rp 16,021,079 6.213703 Rp 2,578,346 62 57 Rp 17,202,902 6.178113 Rp 2,784,491 Rp 17,167,907 6.168017 Rp 2,783,376 63 58 Rp 18,458,160 6.128621 Rp 3,011,797 Rp 18,420,628 6.118632 Rp 3,010,579 64 59 Rp 19,823,084 6.074589 Rp 3,263,280 Rp 19,782,796 6.064718 Rp 3,261,948 65 60 Rp 21,297,310 6.015486 Rp 3,540,414 Rp 21,254,052 6.005744 Rp 3,538,954 66 61 Rp 22,879,734 5.95093 Rp 3,844,732 Rp 22,833,297 5.941328 Rp 3,843,130 67 62 Rp 24,575,008 5.880409 Rp 4,179,132 Rp 24,525,178 5.87096 Rp 4,177,371 68 63 Rp 26,398,237 5.803064 Rp 4,549,017 Rp 26,344,784 5.793783 Rp 4,547,078 69 64 Rp 28,345,499 5.719409 Rp 4,956,019 Rp 28,288,185 5.71031 Rp 4,953,879 70 65 Rp 30,436,738 5.627844 Rp 5,408,241 Rp 30,375,315 5.618943 Rp 5,405,877 Usia

Suami

Usia Istri

alpha = -1 dan r(0) = 4.5% alpha = -1 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,160,488 6.261709 Rp 2,421,142 Rp 15,129,573 6.251432 Rp 2,420,177 61 56 Rp 16,253,222 6.218335 Rp 2,613,758 Rp 16,220,102 6.208152 Rp 2,612,710 62 57 Rp 17,426,308 6.171827 Rp 2,823,525 Rp 17,390,818 6.161745 Rp 2,822,385 63 58 Rp 18,708,271 6.121523 Rp 3,056,147 Rp 18,670,186 6.111551 Rp 3,054,902 64 59 Rp 20,102,884 6.066563 Rp 3,313,719 Rp 20,061,977 6.05671 Rp 3,312,355 65 60 Rp 21,609,888 6.006396 Rp 3,597,812 Rp 21,565,940 5.996674 Rp 3,596,317 66 61 Rp 23,227,954 5.940618 Rp 3,910,023 Rp 23,180,749 5.931039 Rp 3,908,379

67 62 Rp 24,961,597 5.868706 Rp 4,253,339 Rp 24,910,916 5.859284 Rp 4,251,529 68 63 Rp 26,825,687 5.789788 Rp 4,633,276 Rp 26,771,296 5.780537 Rp 4,631,282 69 64 Rp 28,815,177 5.704406 Rp 5,051,389 Rp 28,756,835 5.695341 Rp 5,049,186 70 65 Rp 30,949,308 5.610953 Rp 5,515,874 Rp 30,886,767 5.60209 Rp 5,513,437 Usia

Suami

Usia Istri

alpha = 1 dan r(0) = 4.5% alpha = 1 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,765,839 6.245772 Rp 2,524,242 Rp 15,733,575 6.23553 Rp 2,523,214 61 56 Rp 16,940,248 6.200134 Rp 2,732,239 Rp 16,905,599 6.189992 Rp 2,731,118 62 57 Rp 18,204,889 6.151082 Rp 2,959,624 Rp 18,167,667 6.141047 Rp 2,958,399 63 58 Rp 19,591,050 6.097874 Rp 3,212,767 Rp 19,551,001 6.087955 Rp 3,211,423 64 59 Rp 21,103,844 6.039549 Rp 3,494,275 Rp 21,060,713 6.029757 Rp 3,492,796 65 60 Rp 22,743,961 5.975462 Rp 3,806,227 Rp 22,697,494 5.965809 Rp 3,804,596 66 61 Rp 24,509,795 5.905116 Rp 4,150,604 Rp 24,459,745 5.895617 Rp 4,148,802 67 62 Rp 26,405,883 5.827921 Rp 4,530,926 Rp 26,352,000 5.818591 Rp 4,528,932 68 63 Rp 28,446,814 5.742937 Rp 4,953,357 Rp 28,388,836 5.733791 Rp 4,951,146 69 64 Rp 30,623,724 5.650764 Rp 5,419,395 Rp 30,561,389 5.641819 Rp 5,416,939 70 65 Rp 32,953,381 5.549739 Rp 5,937,825 Rp 32,886,428 5.541013 Rp 5,935,093

Lampiran 8: Nilai Premi Tunggal, Anuitas, dan Premi Tahunan untuk suku bunga Langevin (untuk 𝑟(0) = 5% 𝑑𝑎𝑛 5.55%) Usia

Suami

Usia Istri

alpha = -3.367 dan r(0) = 5% alpha = -3.367 dan r(0) = 5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,258,577 6.265252 Rp 2,275,818 Rp 14,195,153 6.242693 Rp 2,273,883 61 56 Rp 15,251,085 6.225098 Rp 2,449,935 Rp 15,183,310 6.202729 Rp 2,447,843 62 57 Rp 16,315,262 6.182115 Rp 2,639,107 Rp 16,242,810 6.159951 Rp 2,636,841 63 58 Rp 17,477,330 6.135731 Rp 2,848,451 Rp 17,399,759 6.113788 Rp 2,845,987 64 59 Rp 18,740,350 6.085197 Rp 3,079,662 Rp 18,657,221 6.063494 Rp 3,076,975 65 60 Rp 20,103,843 6.030052 Rp 3,333,942 Rp 20,014,727 6.008612 Rp 3,331,007 66 61 Rp 21,567,748 5.969974 Rp 3,612,704 Rp 21,472,220 5.94882 Rp 3,609,492 67 62 Rp 23,137,385 5.904481 Rp 3,918,614 Rp 23,035,002 5.883639 Rp 3,915,094 68 63 Rp 24,828,911 5.832744 Rp 4,256,815 Rp 24,719,193 5.812242 Rp 4,252,953 69 64 Rp 26,642,523 5.755154 Rp 4,629,333 Rp 26,524,946 5.735021 Rp 4,625,083 70 65 Rp 28,600,622 5.670123 Rp 5,044,092 Rp 28,474,631 5.650393 Rp 5,039,407 Usia

Suami

Usia Istri

alpha = -3 dan r(0) = 5% alpha = -3 dan r(0) = 5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,384,926 6.261494 Rp 2,297,363 Rp 14,320,893 6.238954 Rp 2,295,400 61 56 Rp 15,390,742 6.220892 Rp 2,474,041 Rp 15,322,293 6.198545 Rp 2,471,918 62 57 Rp 16,469,184 6.177424 Rp 2,666,028 Rp 16,395,991 6.155284 Rp 2,663,726 63 58 Rp 17,646,721 6.130506 Rp 2,878,510 Rp 17,568,336 6.108589 Rp 2,876,006 64 59 Rp 18,926,480 6.079374 Rp 3,113,229 Rp 18,842,458 6.0577 Rp 3,110,497 65 60 Rp 20,307,982 6.023556 Rp 3,371,428 Rp 20,217,889 6.002148 Rp 3,368,442 66 61 Rp 21,790,955 5.96272 Rp 3,654,533 Rp 21,694,360 5.941602 Rp 3,651,265 67 62 Rp 23,380,576 5.896381 Rp 3,965,242 Rp 23,277,034 5.875579 Rp 3,961,658 68 63 Rp 25,092,777 5.823706 Rp 4,308,730 Rp 24,981,807 5.803249 Rp 4,304,797

69 64 Rp 26,926,974 5.745113 Rp 4,686,935 Rp 26,808,052 5.72503 Rp 4,682,605 70 65 Rp 28,905,109 5.659014 Rp 5,107,799 Rp 28,777,687 5.639339 Rp 5,103,025 Usia

Suami

Usia Istri

alpha = -2.5 dan r(0) = 5% alpha = -2.5 dan r(0) = 5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,561,681 6.256321 Rp 2,327,515 Rp 14,496,793 6.233806 Rp 2,325,512 61 56 Rp 15,586,755 6.215088 Rp 2,507,890 Rp 15,517,360 6.192769 Rp 2,505,722 62 57 Rp 16,685,964 6.170933 Rp 2,703,961 Rp 16,611,725 6.148824 Rp 2,701,610 63 58 Rp 17,886,164 6.123253 Rp 2,921,023 Rp 17,806,626 6.101371 Rp 2,918,463 64 59 Rp 19,190,593 6.071266 Rp 3,160,888 Rp 19,105,301 6.049632 Rp 3,158,093 65 60 Rp 20,598,790 6.014481 Rp 3,424,866 Rp 20,507,300 5.993118 Rp 3,421,808 66 61 Rp 22,110,194 5.952552 Rp 3,714,406 Rp 22,012,070 5.931484 Rp 3,711,056 67 62 Rp 23,729,793 5.884988 Rp 4,032,258 Rp 23,624,583 5.864242 Rp 4,028,583 68 63 Rp 25,473,217 5.810951 Rp 4,383,657 Rp 25,360,435 5.790556 Rp 4,379,620 69 64 Rp 27,338,784 5.73089 Rp 4,770,425 Rp 27,217,909 5.710876 Rp 4,765,978 70 65 Rp 29,347,786 5.64322 Rp 5,200,539 Rp 29,218,274 5.623621 Rp 5,195,633 Usia

Suami

Usia Istri

alpha = -2 dan r(0) = 5% alpha = -2 dan r(0) = 5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,741,634 6.251152 Rp 2,358,227 Rp 14,675,874 6.228662 Rp 2,356,184 61 56 Rp 15,787,091 6.20927 Rp 2,542,503 Rp 15,716,726 6.18698 Rp 2,540,290 62 57 Rp 16,908,423 6.164405 Rp 2,742,913 Rp 16,833,110 6.142328 Rp 2,740,510 63 58 Rp 18,132,944 6.115935 Rp 2,964,869 Rp 18,052,214 6.094089 Rp 2,962,250 64 59 Rp 19,464,029 6.063054 Rp 3,210,268 Rp 19,377,418 6.041461 Rp 3,207,406 65 60 Rp 20,901,259 6.005256 Rp 3,480,494 Rp 20,808,313 5.983938 Rp 3,477,361 66 61 Rp 22,443,795 5.942175 Rp 3,777,034 Rp 22,344,067 5.921157 Rp 3,773,598 67 62 Rp 24,096,441 5.873313 Rp 4,102,700 Rp 23,989,473 5.852624 Rp 4,098,926

68 63 Rp 25,874,542 5.797824 Rp 4,462,802 Rp 25,759,841 5.777494 Rp 4,458,653 69 64 Rp 27,775,288 5.716191 Rp 4,859,055 Rp 27,652,335 5.696249 Rp 4,854,482 70 65 Rp 29,819,300 5.626824 Rp 5,299,490 Rp 29,687,553 5.607306 Rp 5,294,441 Usia

Suami

Usia Istri

alpha = -1.5 dan r(0) = 5% alpha = -1.5 dan r(0) = 5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,921,826 6.246074 Rp 2,388,993 Rp 14,855,191 6.223609 Rp 2,386,909 61 56 Rp 15,988,498 6.203537 Rp 2,577,320 Rp 15,917,156 6.181275 Rp 2,575,060 62 57 Rp 17,133,015 6.15795 Rp 2,782,260 Rp 17,056,614 6.135905 Rp 2,779,804 63 58 Rp 18,383,206 6.108673 Rp 3,009,362 Rp 18,301,266 6.086863 Rp 3,006,683 64 59 Rp 19,742,626 6.054875 Rp 3,260,616 Rp 19,654,668 6.033322 Rp 3,257,686 65 60 Rp 21,210,922 5.99603 Rp 3,537,494 Rp 21,116,480 5.974757 Rp 3,534,283 66 61 Rp 22,786,997 5.931754 Rp 3,841,528 Rp 22,685,615 5.910788 Rp 3,838,002 67 62 Rp 24,475,494 5.861539 Rp 4,175,609 Rp 24,366,702 5.840907 Rp 4,171,732 68 63 Rp 26,291,488 5.784529 Rp 4,545,139 Rp 26,174,788 5.764264 Rp 4,540,873 69 64 Rp 28,231,039 5.701236 Rp 4,951,740 Rp 28,105,906 5.681368 Rp 4,947,032 70 65 Rp 30,314,072 5.610068 Rp 5,403,513 Rp 30,179,969 5.590632 Rp 5,398,311 Usia

Suami

Usia Istri

alpha = -1 dan r(0) = 5% alpha = -1 dan r(0) = 5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,098,748 6.241184 Rp 2,419,212 Rp 15,031,252 6.218743 Rp 2,417,088 61 56 Rp 16,187,080 6.197998 Rp 2,611,663 Rp 16,114,774 6.175763 Rp 2,609,357 62 57 Rp 17,355,433 6.151693 Rp 2,821,245 Rp 17,277,952 6.129679 Rp 2,818,737 63 58 Rp 18,632,213 6.101607 Rp 3,053,657 Rp 18,549,064 6.079832 Rp 3,050,917 64 59 Rp 20,021,191 6.046886 Rp 3,310,992 Rp 19,931,883 6.025372 Rp 3,307,992 65 60 Rp 21,522,121 5.986981 Rp 3,594,821 Rp 21,426,173 5.965753 Rp 3,591,529 66 61 Rp 23,133,683 5.921488 Rp 3,906,735 Rp 23,030,625 5.900573 Rp 3,903,117

67 62 Rp 24,860,383 5.849888 Rp 4,249,719 Rp 24,749,735 5.829314 Rp 4,245,737 68 63 Rp 26,717,065 5.771313 Rp 4,629,287 Rp 26,598,316 5.751113 Rp 4,624,899 69 64 Rp 28,698,664 5.686301 Rp 5,046,983 Rp 28,571,287 5.666506 Rp 5,042,135 70 65 Rp 30,824,410 5.593252 Rp 5,511,000 Rp 30,687,866 5.573899 Rp 5,505,638 Usia

Suami

Usia Istri

alpha = 1 dan r(0) = 5% alpha = 1 dan r(0) = 5.55%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,701,405 6.225318 Rp 2,522,185 Rp 15,630,966 6.202956 Rp 2,519,922 61 56 Rp 16,871,052 6.179879 Rp 2,729,997 Rp 16,795,408 6.157734 Rp 2,727,531 62 57 Rp 18,130,555 6.131041 Rp 2,957,174 Rp 18,049,293 6.109129 Rp 2,954,479 63 58 Rp 19,511,071 6.078065 Rp 3,210,080 Rp 19,423,637 6.056406 Rp 3,207,123 64 59 Rp 21,017,708 6.019993 Rp 3,491,317 Rp 20,923,543 5.998612 Rp 3,488,064 65 60 Rp 22,651,164 5.956185 Rp 3,802,965 Rp 22,549,716 5.935109 Rp 3,799,377 66 61 Rp 24,409,843 5.886145 Rp 4,147,000 Rp 24,300,574 5.865404 Rp 4,143,035 67 62 Rp 26,298,277 5.809287 Rp 4,526,937 Rp 26,180,640 5.788913 Rp 4,522,548 68 63 Rp 28,331,029 5.724672 Rp 4,948,935 Rp 28,204,451 5.704702 Rp 4,944,071 69 64 Rp 30,499,237 5.6329 Rp 5,414,482 Rp 30,363,144 5.613368 Rp 5,409,078 70 65 Rp 32,819,671 5.532313 Rp 5,932,360 Rp 32,673,495 5.513259 Rp 5,926,348

Lampiran 9: Nilai Premi Tunggal, Anuitas, dan Premi Tahunan untuk suku bunga Langevin (untuk 𝑟(0) = 6% ) Usia

Suami

Usia Istri

alpha = -3.367 dan r(0) = 6% alpha = -1.5 dan r(0) = 6%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,143,566 6.224342 Rp 2,272,299 Rp 14,800,991 6.205335 Rp 2,385,204 61 56 Rp 15,128,181 6.184534 Rp 2,446,131 Rp 15,859,128 6.163165 Rp 2,573,211 62 57 Rp 16,183,878 6.141922 Rp 2,634,986 Rp 16,994,470 6.117972 Rp 2,777,794 63 58 Rp 17,336,664 6.095938 Rp 2,843,970 Rp 18,234,616 6.069121 Rp 3,004,490 64 59 Rp 18,589,605 6.04584 Rp 3,074,776 Rp 19,583,124 6.015789 Rp 3,255,288 65 60 Rp 19,942,240 5.991172 Rp 3,328,604 Rp 21,039,662 5.957452 Rp 3,531,654 66 61 Rp 21,394,517 5.931612 Rp 3,606,864 Rp 22,603,151 5.893732 Rp 3,835,117 67 62 Rp 22,951,724 5.866684 Rp 3,912,214 Rp 24,278,212 5.824124 Rp 4,168,560 68 63 Rp 24,629,948 5.795565 Rp 4,249,793 Rp 26,079,864 5.747779 Rp 4,537,381 69 64 Rp 26,429,308 5.718643 Rp 4,621,604 Rp 28,004,124 5.665205 Rp 4,943,179 70 65 Rp 28,372,149 5.634343 Rp 5,035,574 Rp 30,070,889 5.574821 Rp 5,394,055 Usia

Suami

Usia Istri

alpha = -3 dan r(0) = 6% alpha = -1 dan r(0) = 6%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,268,809 6.220618 Rp 2,293,793 Rp 14,976,353 6.200489 Rp 2,415,350 61 56 Rp 15,266,617 6.180366 Rp 2,470,180 Rp 16,055,961 6.157676 Rp 2,607,471 62 57 Rp 16,336,456 6.137273 Rp 2,661,843 Rp 17,214,930 6.111771 Rp 2,816,684 63 58 Rp 17,504,579 6.09076 Rp 2,873,957 Rp 18,481,432 6.062119 Rp 3,048,675 64 59 Rp 18,774,115 6.040069 Rp 3,108,262 Rp 19,859,241 6.007871 Rp 3,305,537 65 60 Rp 20,144,607 5.984733 Rp 3,365,999 Rp 21,348,130 5.948484 Rp 3,588,835 66 61 Rp 21,615,790 5.924422 Rp 3,648,590 Rp 22,946,798 5.883558 Rp 3,900,157 67 62 Rp 23,192,814 5.858656 Rp 3,958,726 Rp 24,659,734 5.812578 Rp 4,242,478 68 63 Rp 24,891,543 5.786608 Rp 4,301,578 Rp 26,501,727 5.734681 Rp 4,621,308

69 64 Rp 26,711,321 5.708692 Rp 4,679,062 Rp 28,467,680 5.650403 Rp 5,038,168 70 65 Rp 28,674,041 5.623333 Rp 5,099,118 Rp 30,576,802 5.558155 Rp 5,501,250 Usia

Suami

Usia Istri

alpha = -2.5 dan r(0) = 6% alpha = 1 dan r(0) = 6%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,444,014 6.215491 Rp 2,323,874 Rp 15,573,673 6.184765 Rp 2,518,070 61 56 Rp 15,460,914 6.174613 Rp 2,503,949 Rp 16,733,880 6.139719 Rp 2,725,512 62 57 Rp 16,551,340 6.130839 Rp 2,699,686 Rp 17,983,196 6.091304 Rp 2,952,273 63 58 Rp 17,741,930 6.083572 Rp 2,916,367 Rp 19,352,520 6.038787 Rp 3,204,703 64 59 Rp 19,035,924 6.032033 Rp 3,155,806 Rp 20,846,952 5.98122 Rp 3,485,402 65 60 Rp 20,432,883 5.975739 Rp 3,419,306 Rp 22,467,201 5.917964 Rp 3,796,441 66 61 Rp 21,932,256 5.914345 Rp 3,708,315 Rp 24,211,697 5.848532 Rp 4,139,791 67 62 Rp 23,539,005 5.847365 Rp 4,025,575 Rp 26,084,956 5.77234 Rp 4,518,957 68 63 Rp 25,268,698 5.773965 Rp 4,376,316 Rp 28,101,494 5.688456 Rp 4,940,091 69 64 Rp 27,119,589 5.694595 Rp 4,762,338 Rp 30,252,449 5.597479 Rp 5,404,656 70 65 Rp 29,112,929 5.607678 Rp 5,191,619 Rp 32,554,597 5.49776 Rp 5,921,430 Usia

Suami

Usia Istri

alpha = -2 dan r(0) = 6%

Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,622,386 6.210368 Rp 2,354,512 61 56 Rp 15,659,492 6.168848 Rp 2,538,479 62 57 Rp 16,771,850 6.12437 Rp 2,738,543 63 58 Rp 17,986,549 6.076319 Rp 2,960,106 64 59 Rp 19,306,970 6.023895 Rp 3,205,064 65 60 Rp 20,732,711 5.966596 Rp 3,474,797 66 61 Rp 22,262,949 5.90406 Rp 3,770,786 67 62 Rp 23,902,465 5.835793 Rp 4,095,838

72 68 63 Rp 25,666,544 5.760955 Rp 4,455,258 69 64 Rp 27,552,324 5.680026 Rp 4,850,739 70 65 Rp 29,580,389 5.591428 Rp 5,290,310

Lampiran 10: Nilai Premi Tunggal, Anuitas, dan Premi Tahunan untuk suku bunga CIR (untuk 𝑟(0) = 4.5% dan 4.75%) Usia

Suami

Usia Istri

alpha = -3.367 dan r(0) = 4.5% alpha = -3.367 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 14,991,810 6.536959 Rp 2,293,392 Rp 14,935,428 6.51733 Rp 2,291,648 61 56 Rp 16,034,757 6.494567 Rp 2,468,949 Rp 15,974,531 6.475114 Rp 2,467,066 62 57 Rp 17,153,194 6.449188 Rp 2,659,745 Rp 17,088,835 6.429922 Rp 2,657,705 63 58 Rp 18,374,471 6.400216 Rp 2,870,914 Rp 18,305,584 6.381153 Rp 2,868,695 64 59 Rp 19,701,492 6.346867 Rp 3,104,129 Rp 19,627,691 6.328025 Rp 3,101,709 65 60 Rp 21,134,360 6.288653 Rp 3,360,714 Rp 21,055,270 6.270051 Rp 3,358,070 66 61 Rp 22,673,552 6.225224 Rp 3,642,207 Rp 22,588,803 6.206885 Rp 3,639,314 67 62 Rp 24,324,033 6.156071 Rp 3,951,227 Rp 24,233,250 6.138017 Rp 3,948,058 68 63 Rp 26,101,893 6.080322 Rp 4,292,847 Rp 26,004,675 6.06258 Rp 4,289,374 69 64 Rp 28,008,113 5.998384 Rp 4,669,277 Rp 27,904,017 5.98098 Rp 4,665,459 70 65 Rp 30,065,812 5.908584 Rp 5,088,497 Rp 29,954,383 5.891549 Rp 5,084,297 Usia

Suami

Usia Istri

alpha = -3 dan r(0) = 4.5% alpha = -3 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,125,031 6.532994 Rp 2,315,176 Rp 15,068,085 6.513383 Rp 2,313,404 61 56 Rp 16,182,021 6.49013 Rp 2,493,328 Rp 16,121,173 6.470696 Rp 2,491,412 62 57 Rp 17,315,517 6.444239 Rp 2,686,976 Rp 17,250,475 6.424995 Rp 2,684,901 63 58 Rp 18,553,132 6.394702 Rp 2,901,329 Rp 18,483,495 6.375663 Rp 2,899,070 64 59 Rp 19,897,839 6.340722 Rp 3,138,103 Rp 19,823,216 6.321906 Rp 3,135,639 65 60 Rp 21,349,750 6.281796 Rp 3,398,669 Rp 21,269,760 6.263225 Rp 3,395,976 66 61 Rp 22,909,124 6.217567 Rp 3,684,580 Rp 22,823,396 6.199261 Rp 3,681,632 67 62 Rp 24,580,774 6.147519 Rp 3,998,487 Rp 24,488,930 6.129503 Rp 3,995,255 68 63 Rp 26,380,542 6.07078 Rp 4,345,495 Rp 26,282,180 6.053079 Rp 4,341,952

69 64 Rp 28,308,586 5.987781 Rp 4,727,726 Rp 28,203,266 5.970423 Rp 4,723,831 70 65 Rp 30,387,545 5.896851 Rp 5,153,181 Rp 30,274,818 5.879867 Rp 5,148,895 Usia

Suami

Usia Istri

alpha = -2.5 dan r(0) = 4.5% alpha = -2.5 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,311,368 6.527537 Rp 2,345,658 Rp 15,253,631 6.50795 Rp 2,343,846 61 56 Rp 16,388,676 6.484007 Rp 2,527,554 Rp 16,326,953 6.464599 Rp 2,525,594 62 57 Rp 17,544,091 6.43739 Rp 2,725,342 Rp 17,478,083 6.418176 Rp 2,723,217 63 58 Rp 18,805,636 6.38705 Rp 2,944,338 Rp 18,734,934 6.368044 Rp 2,942,023 64 59 Rp 20,176,401 6.332166 Rp 3,186,335 Rp 20,100,606 6.313388 Rp 3,183,807 65 60 Rp 21,656,529 6.27222 Rp 3,452,769 Rp 21,575,254 6.25369 Rp 3,450,004 66 61 Rp 23,245,990 6.206836 Rp 3,745,224 Rp 23,158,855 6.188577 Rp 3,742,194 67 62 Rp 24,949,387 6.135494 Rp 4,066,402 Rp 24,856,011 6.117529 Rp 4,063,080 68 63 Rp 26,782,231 6.057313 Rp 4,421,470 Rp 26,682,210 6.039671 Rp 4,417,825 69 64 Rp 28,743,527 5.972763 Rp 4,812,434 Rp 28,636,424 5.955469 Rp 4,808,424 70 65 Rp 30,855,235 5.880171 Rp 5,247,336 Rp 30,740,607 5.863258 Rp 5,242,922 Usia

Suami

Usia Istri

alpha = -2 dan r(0) = 4.5% alpha = -2 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,501,039 6.522085 Rp 2,376,700 Rp 15,442,493 6.502522 Rp 2,374,847 61 56 Rp 16,599,846 6.47787 Rp 2,562,547 Rp 16,537,225 6.45849 Rp 2,560,541 62 57 Rp 17,778,606 6.430504 Rp 2,764,730 Rp 17,711,603 6.41132 Rp 2,762,552 63 58 Rp 19,065,822 6.37933 Rp 2,988,687 Rp 18,994,019 6.360358 Rp 2,986,313 64 59 Rp 20,464,736 6.323503 Rp 3,236,297 Rp 20,387,722 6.304763 Rp 3,233,702 65 60 Rp 21,975,542 6.262486 Rp 3,509,076 Rp 21,892,923 6.243998 Rp 3,506,235 66 61 Rp 23,597,934 6.195886 Rp 3,808,646 Rp 23,509,321 6.177674 Rp 3,805,530 67 62 Rp 25,336,318 6.123172 Rp 4,137,777 Rp 25,241,325 6.105261 Rp 4,134,357

68 63 Rp 27,205,886 6.043458 Rp 4,501,709 Rp 27,104,105 6.025876 Rp 4,497,953 69 64 Rp 29,204,465 5.957244 Rp 4,902,345 Rp 29,095,459 5.940018 Rp 4,898,211 70 65 Rp 31,353,308 5.862858 Rp 5,347,785 Rp 31,236,639 5.84602 Rp 5,343,232 Usia

Suami

Usia Istri

alpha = -1.5 dan r(0) = 4.5% alpha = -1.5 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,690,922 6.516729 Rp 2,407,791 Rp 15,631,565 6.497189 Rp 2,405,896 61 56 Rp 16,812,101 6.471823 Rp 2,597,738 Rp 16,748,575 6.452469 Rp 2,595,685 62 57 Rp 18,015,318 6.423695 Rp 2,804,510 Rp 17,947,307 6.404541 Rp 2,802,278 63 58 Rp 19,329,622 6.371669 Rp 3,033,683 Rp 19,256,698 6.352731 Rp 3,031,247 64 59 Rp 20,758,445 6.314875 Rp 3,287,230 Rp 20,680,185 6.296172 Rp 3,284,565 65 60 Rp 22,302,067 6.252753 Rp 3,566,759 Rp 22,218,065 6.234308 Rp 3,563,838 66 61 Rp 23,959,924 6.184891 Rp 3,873,945 Rp 23,869,784 6.166727 Rp 3,870,738 67 62 Rp 25,736,248 6.110747 Rp 4,211,637 Rp 25,639,574 6.092891 Rp 4,208,113 68 63 Rp 27,645,937 6.029426 Rp 4,585,169 Rp 27,542,316 6.011905 Rp 4,581,296 69 64 Rp 29,685,626 5.941458 Rp 4,996,353 Rp 29,574,620 5.924301 Rp 4,992,086 70 65 Rp 31,875,849 5.845167 Rp 5,453,368 Rp 31,757,025 5.828406 Rp 5,448,664 Usia

Suami

Usia Istri

alpha = -1 dan r(0) = 4.5% alpha = -1 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 15,877,319 6.511573 Rp 2,438,323 Rp 15,817,163 6.492056 Rp 2,436,387 61 56 Rp 17,021,333 6.465982 Rp 2,632,444 Rp 16,956,911 6.446654 Rp 2,630,343 62 57 Rp 18,249,685 6.417096 Rp 2,843,916 Rp 18,180,672 6.397971 Rp 2,841,631 63 58 Rp 19,592,036 6.364217 Rp 3,078,468 Rp 19,517,991 6.345312 Rp 3,075,971 64 59 Rp 21,052,049 6.306449 Rp 3,338,178 Rp 20,972,538 6.287783 Rp 3,335,443 65 60 Rp 22,630,130 6.243208 Rp 3,624,760 Rp 22,544,733 6.224805 Rp 3,621,758 66 61 Rp 24,325,496 6.174061 Rp 3,939,950 Rp 24,233,806 6.155945 Rp 3,936,651

67 62 Rp 26,142,235 6.098455 Rp 4,286,698 Rp 26,043,845 6.080652 Rp 4,283,068 68 63 Rp 28,094,986 6.01548 Rp 4,670,448 Rp 27,989,476 5.99802 Rp 4,666,453 69 64 Rp 30,179,208 5.925695 Rp 5,092,939 Rp 30,066,138 5.908606 Rp 5,088,533 70 65 Rp 32,414,712 5.827417 Rp 5,562,450 Rp 32,293,648 5.810732 Rp 5,557,587 Usia

Suami

Usia Istri

alpha = 1 dan r(0) = 4.5% alpha = 1 dan r(0) = 4.75%

Premi Tunggal Anuitas Premi Tahunan Premi Tunggal Anuitas Premi Tahunan 60 55 Rp 16,511,895 6.494848 Rp 2,542,307 Rp 16,448,995 6.475404 Rp 2,540,227 61 56 Rp 17,741,560 6.446881 Rp 2,751,960 Rp 17,674,028 6.427637 Rp 2,749,693 62 57 Rp 19,065,946 6.395325 Rp 2,981,232 Rp 18,993,412 6.376295 Rp 2,978,754 63 58 Rp 20,517,615 6.339398 Rp 3,236,524 Rp 20,439,581 6.320601 Rp 3,233,803 64 59 Rp 22,101,647 6.278096 Rp 3,520,438 Rp 22,017,616 6.259554 Rp 3,517,442 65 60 Rp 23,819,503 6.210738 Rp 3,835,213 Rp 23,728,991 6.192477 Rp 3,831,906 66 61 Rp 25,670,180 6.136794 Rp 4,182,995 Rp 25,572,717 6.118841 Rp 4,179,340 67 62 Rp 27,657,798 6.055638 Rp 4,567,280 Rp 27,552,920 6.038023 Rp 4,563,235

Dalam dokumen EVALUASI PREMI POLIS JOINT LIFE PASANGAN SUAMI ISTRI MENGGUNAKAN COPULA FRANK SUKU BUNGA STOKASTIK SKRIPSI (Halaman 60-98)