Hospital care is one of the insurance products giving compensation to the members by reimbursing the medicine and hospital care costs.&nbsp; According to the number of members in one insurance policy, health insurance is classified into two categories namely individual health insurance and joint health insurance. This article discusses the monthly premium of joint health insurance. The monthly premium of joint term health insurance is calculated before deciding the probability to facilitate hospital care for two or more people using The RP-2000 Combined Healthy Tables and joint life annuity. Based on the simulation, at the same benefit, the monthly premium that must be paid for joint health insurance is smaller than for individual health insurance because the premium for joint insurance are borne by some insured under the same insurance polic

Ekawati, Darma

English

Open Journal System (OJS) Universitas Bumigora

Jurnal Varianhttps://journal.universitasbumigora.ac.id/index.php/Variane-ISSN 2581-2017Vol. 4, No.1, Oktober 2020, Hal. 25-3025The Determination of Monthly Premium of Joint TermHealthInsurance for Hospital CareDarma Ekawati1Mathematics, Universitas Sulawesi Barat, Indonesia, e-mail : darmaekawati@unsulbar.ac.idABSTRACTArticle history:Received : 22-08-2020Revised : 08-09-2020Accepted : 11-09-2020Hospital care is one of the insurance products giving compensation to the members byreimbursing the medicine and hospital care costs. According to the number of members inone insurance policy, health insurance is classified into two categories namely individualhealth insurance and joint health insurance. This article discusses the monthly premium ofjoint health insurance. The monthly premium of joint term health insurance is calculatedbefore deciding the probability to facilitate hospital care for two or more people using TheRP-2000 Combined Healthy Tables and joint life annuity. Based on the simulation, at the samebenefit, the monthly premium that must be paid for joint health insurance is smaller than forindividual health insurance because the premium for joint insurance are borne by someinsured under the same insurance policyKeyword:Hospital;Health Insurance;Premiums;Medicine;Joint Term InsuranceThis is an open access article under the CC BY-SA license.DOI: https://doi.org/10.30812/varian.v4i1.844————————————————————A. INTRODUCTIONEach human will obviously face risks in their life. A risk is the uncertainty of an event that possiblybrings disadvantages. Risks faced by each person are various. One of them is the attack of disease and no oneknows when they will experience it. Once it happens, they must solve it by finding out medication so thatthey can go back to their normal daily routines.Health insurance is a facility to minimize or to solve the risk of sickness and costs it results. Based on theinsurance contract, members have to pay a particular amount of money or premium every period to theinsurance company. In return, they will get a benefit in the form of compensation to subsidize or toreimburse the whole cost spent for health care when getting ill.Health insurance is a part of life insurance with life as an object. The purpose of health insurance is totransfer the risk of illness from the insured to the insurer. Thus, the insurer has the responsibility to provide(cost of) healthcare service to the insured when sick. It is to protect the community from (economic)difficulties to pay the health care costs (Suryono, 2009).Health insurance has some types. Based on the kinds of treatment, it is divided into two categories,inpatient health insurance, and outpatient health insurance. While according to the number of members inone insurance policy, it is categorized into individual and joint health insurance.26 |Jurnal Varian| Vol. 4, No. 1, Oktober 2020, Hal. 25-30Health insurance for hospital care provides compensation for health by giving a particular amount ofmoney to pay medicine and other health care when somebody is sick (Wilandari, 2007). Joint healthinsurance bears 2 or more persons (Gunanto, Hasriati, & Pane, 2014).Studies related to health insurance for hospital care have been widely carried out includinginvestigating the individual health insurance premium for hospital care (Wilandari, 2007), cost-sharingmachanisms in health insurance schemes (Qingyue, Liying, & Beibei, 2011) and public and private healthinsuranse premiums (Guy, Adams, & Atherly, 2012) . It was followed up about studying the formulation ofmonthly individual health insurance for hospital care (Lahallo, Widana, & Nilakusmawati, 2013), the effect ofchange in interest rate on the calculation of annual premium individual health insurance (Pradipta, Widana,& Sugiarto, 2013), comparison of the health insurance premiums of business entity BPJS participants withprivate health insurance (Dewi & Sulistyani, 2015). While related to joint health insurance, studied about itspurpose for hospital care (Munadi & Sunarsih, 2009), the annual premium reserves for joint healthinsurance (Gunanto et al., 2014), research that discusses the determination of individual and annual healthinsurance premiums under individual and joint status (Hayuningtias, Ruswandi, Warsono, & Nusyirwan,2019).This study basically aimed at continuing the study about the determination of monthly premium forhospital care of individual term health insurance (Espinoza, 2016) ,while the current research investigatedthat of joint term health insurance. The purpose of this study was to compare the monthly premium thatmust be paid by each family member as a member of individual health insurance and the premium they mustpay for joint status.B. LITERATURE REVIEW1. Life Annuities with m-thly PaymentsAn annuity is a payment series with a particular amount of money paid every an interval and duringa period (Juliandi, Satyahadewi, & Mara, 2015). It is an important component in calculating theinsurance premium. One of the annuity systems mostly applied by a life annuity is that the paymentdepends on the life and death of a person (Juliandi et al., 2015). The life annuity is paid once in a year,at the beginning of the year by a person aged X during n years. It is also usually referred to as annuitycalculated using the following formula (1) (Bowers, Gerber, & Hickman, 1997):    : | =  =0 −1        (1)  = 11+ ,   is the annual interest rate, and     the probability of a person aged  will attain ages   +  ൥Based on the annuity formula above, another equation to calculate the annuity with  – thly paymentin a year can be derived (Juliandi et al., 2015):    : |( ) =     =0   −1           (2)Using the commutation symbol, equation (2) can be presented as below (Espinoza, 2016):    : |( ) =   −  +   −  −1  1 −   +   (3)If the annuity payment is made every month or 12 times in a year, the amount of the monthly annuityfor   years is:   : |(1 ) =   −  +   − 11  1 −   +   (4)2. Monthly Premium of Health InsuranceThe insurance premium is the payment that must be made by insurance members (insured) to theinsurance party (insurer) under the coverage agreement signed on the insurance contract letter.Based on payment time, the premium can be paid once (single premium) or periodically (annual ormonthly premium). The single premium of term health insurance for hospital care for individualmember aged  , with     the average days staying in the hospital and      the probability of a personDarma Ekawati, The Determination of...27aged   to be hospitalized during n years of coverage can be calculated using the following formula(Wilandari, 2007):  : |1 =     =0 −1   +1          +    (5)Using the commutation symbol, we obtain (Espinoza, 2016)  : |1 = 1       =0 −1  +     +    (6)The monthly premium is paid at the beginning of each month by an insurance member during   years. Thecalculation of monthly premium during   years of the term insurance contract is based on the term annuityof   years paid 12 times in a year.The amount of health insurance premium with the term of   years for hospital care that must be paid by aninsurance member aged  when the insurance contract is signed or the benefit of   is formulated (7):  : |1(1 ) =    : |11     : |(1 ) =       =0 −1  +     +   1    −  + −11     −  + (7)3. Commutation SymbolThe symbol of commutation is made to assist the calculation of insurance value like an annuity, andpremium (Sari & Jazwinarti, 2016).Symbols of commutation in joint insurance covering m persons are defined analogously with thecommutation symbol of individual insurance (Sari & Jazwinarti, 2016), as formula (8) and (9):  1           =   1              1           (8)and  1           =  =0  1 + ৓   + ৓   + ৓ ৓   +   (9)C. RESEARCH METHODThis is a literature review started by collecting materials from various supporting resources,formulating problems, and establishing steps and formula to determine the monthly premium of joint termhealth insurance for hospital care. The last step was to use the equation into a relevant case illustration orsimulation.D. RESULTS AND DISCUSSION1. Joint Mortality TablesSimilarly, with a single mortality table, that table for joint mortality presents the death rate todetermine the insurance premium (Futami, 1993). In the joint mortality table of some persons aged 1           , ( 1         …    are independent), the function of the number of people aged  1 ismultiplied with the function of the number of people aged           years notated with   1           isformulated (10) and (11):  1           =   1൥          (10)The probability of persons aged  1         ൥   years to stay alive until 1 year later is:  1           =   1 ൥          (11)2. Monthly Premium of Term Joint Health Insurance for Hospital CareJoint health insurance covers 2 or more people. The calculation of life annuity of joint healthinsurance is analogous with individual health insurance. Based on equation (6), the single premium ofjoint health insurance coveringmmembers aged  1          and    can be equated formulate (12):  1          : | 1 = 1  1               =0 −1  1 + ৓   + ৓ ৓   +     1 + ৓   + ৓   + ৓ ৓   +    (12)and based on equation (4) the term annuity of joint insurance covering more than two persons aged 1        and    years paid at the beginning of each month for   years is:28 |Jurnal Varian| Vol. 4, No. 1, Oktober 2020, Hal. 25-30    1          : |1  =  1          −  1+ ৓  + ৓  + ৓ ৓  +   1          − 11  1 −  1+ ৓  + ৓  + ৓ ৓  +   1          (13)thus, the premium rate of terms joint health insurance of n years for hospital care that must be paid bythe members with benefit B is formulated (14):  1        : |1(1 ) =  1       : |1    1       : |(1 ) =       =0 −1  1+ ৓  + ৓ ৓  +     1+ ৓  + ৓ ৓  +   1    1       −  1+ ৓  + ৓ ৓  + −11     1       −  1+ ৓  + ৓ ৓  + (14)3. Case SimulationThere are two families and each of them has 5 members. The first family consists of an old man aged60, an old woman aged 58, a middle-age man aged 35, a middle-aged woman aged 32, and a boy aged 7.The second family consists of a middle-age man aged 45, a middle-aged woman aged 40, a teenager aged17, and two boys aged 15 and 10. Both families apply for the health insurance policy for hospital care for10 years with the room compensation of Rp 700,000, doctor visit of Rp 150,000/day (maximum of 180days in a year), and care cost per period per year of Rp 5,000,000. Based on the Indonesian MortalityTable 2011, RP-2000 Combined healthy table, and the interest rate of 6%, we obtained the data Table 1,2and 3:1) Individual health insuranceBased on the available data, it is obtained that the premium must be paid by each health insuranceparticipant presented in the following Table 1:Table 1. The Monthly Premium of Health Insurance for Hospital Care for 10 Years of Each MemberFamily members Individual Monthly PremiumThe 1st family The 2nd familyI Rp 113.788 Rp 31.713II Rp 70.670 Rp 15.796III Rp 15.519 Rp 2.925IV Rp 7.869 Rp 4.901V Rp 3.510 Rp 3.894Total of premium Rp 211.356 Rp 59.2292) Joint health insuranceBased on the available data, a table containing the data of combined healthy and commutation of thefirst family under a joint insurance is as Table 2:Table 2. Combined Healthy and Commutation of the First Family under a Joint Insurance                                                60 58 35 32 7 7,51005 10   7,73952 10   7,30143 10   0,00993461 59 36 33 8 7,33281 10   7,12912 10   6,72559 10   0,01088362 60 37 34 9 7,14804 10   6,55611 10   6,18501 10   0,01189363 61 38 35 10 6,95522 10   6,01817 10   5,67752 10   0,01295064 62 39 36 11 6,75348 10   5,51284 10   5,20079 10   0,01402665 63 40 37 12 6,54145 10   5,03751 10   4,75237 10   0,01510766 64 41 38 13 6,31673 10   4,58911 10   4,32935 10   0,01618667 65 42 39 14 6,07936 10   4,16666 10   3,93081 10   0,01725668 66 43 40 15 5,83004 10   3,7696 10   3,55623 10   0,01830969 67 44 41 16 5,56913 10   3,39708 10   3,2048 10   0,019344and a table containing the data of combined healthy and commutation of the second family under ajoint insurance is Table 3:Darma Ekawati, The Determination of...29Table 3. Combined Healthy and Commutation of the secondf family under a Joint Insurance                                                45 40 17 15 10 9,08176 10   2,06729 10   1,95027 10   0,00287946 41 18 16 11 9,03886 10   1,94106 10   1,83119 10   0,00309447 42 19 17 12 8,99157 10   1,82161 10   1,7185 10   0,00333348 43 20 18 13 8,93896 10   1,70844 10   1,61174 10   0,00358949 44 21 19 14 8,88007 10   1,60112 10   1,51049 10   0,00386650 45 22 20 15 8,81422 10   1,49929 10   1,41442 10   0,00415751 46 23 21 16 8,74017 10   1,40254 10   1,32315 10   0,00446252 47 24 22 17 8,65692 10   1,31055 10   1,23637 10   0,00478353 48 25 23 18 8,56386 10   1,22308 10   1,15385 10   0,00512554 49 26 24 19 8,46082 10   1,13996 10   1,07544 10   0,005494Values in tables 2 and 3 are substituted into equation (14) and the monthly premiums of joint healthinsurances were obtained. The first family has to pay Rp 204,709 and the second family pays Rp 57,502Based on the case simulation above, it can be seen that if those families apply for the individual healthinsurance policy for hospital care, the total monthly premiums they must pay are Rp 211.356 for the firstfamily and 59.229 for the second family. Those amounts are higher than the monthly premiums for jointinsurance that are Rp 204.709 for the first family and Rp 57.502 for the second family.The monthly premium paid for joint health insurance is lower than for individual health insurancebecause the premium for joint insurance are borne by some insured under the same insurance policy sothat the premium will be smaller. In the above cases, although both families consist of the same numberof members, the first family will pay higher than the second family when they apply for individual or jointinsurance because the first family has 2 elderlies. The probability of elder persons attacked with anillness and requiring hospital care is higher than middle-aged persons, teenagers, or children.The previous research finding was only to calculate the monthly premium of health insurance that mustbe paid by one person, while the result of the current study can be applied for the joint insurancepremium covering 2 or more members.E. CONCLUSION AND SUGGESTIONThe amount of monthly premium of n year joint term health insurance for hospital care is influenced bythe amount of compensation provided by the insurance company, the average number of days of hospitalcare, and the probability of people aged  1          and    years in a particular period to be hospitalized.The monthly premium that must be paid for joint health insurance is smaller than for individual healthinsurance because the premium for joint insurance are borne by some insured under the same insurancepolicy. In both individual and joint health insurance with the same number of family members, the firstfamily pays a higher premium than the second family because the first one has two elderly persons. Theprobabilities of elderlies to be attacked with illness and to require hospital care is higher than middle-agepersons or children.ACKNOWLEDGEMENTSResearchers would like to thank the Universitas Sulawesi Barat for giving permission to collaborate in thefield of research and provide moral support, so that this research can be carried out well.REFERENCESBowers, N. L., Gerber, H. U., & Hickman, J. C. (1997). Actuarial Mathematics. 2nd ed. Schaumburg: The Society ofActuaries.Dewi, M. W., & Sulistyani, D. (2015). Perbandingan Premi Asuransi Kesehatan Peserta Bpjs Badan Usaha DenganAsuransi Kesehatan Swasta. Jurnal Akuntansi Dan Pajak, 16(01), 33–47.Espinoza, E. (2016). Penentuan Premi Bulanan Asuransi Kesehatan Berjangka Perawatan Rumah Sakit UntukPerorangan. Jurnal Matematika Unand, 5(4), 30–35.Futami, T. (1993).Matematika Asuransi Jiwa Bagian I. Tokyo: Oriental Life Insurance Cultural Development Center.Darma Ekawati, The Determination of...30Gunanto, A., Hasriati, & Pane, R. (2014). Cadangan Premi Tahunan Asuransi Kesehatan pada Status Gabungan. JOM31 |Jurnal Varian| Vol. 4, No. 1, Oktober 2020, Hal. 25-30FMIPA, 1(2), 475–483.Guy, G. P., Adams, E. K., & Atherly, A. (2012). Public and Private Health Insurance Premiums: How Do They Affect theHealth Insurance Status of Low-Income Childless Adults? Inquiry: The Journal of Health Care Organization,Provision, and Financing, 49(1), 52–64.Hayuningtias, M., Ruswandi, R., Warsono, W., & Nusyirwan, N. (2019). Menentukan Premi Asuransi Kesehatan untukPerawatan Rumah Sakit pada Status Perorangan dan Joint Life. Seminar Nasional SMIAP V 2019.Juliandi, Satyahadewi, N., & Mara, M. N. (2015). Penentuan Nilai Anuitas Berjangka Individu dengan Metode Woolhouse.Buletin Ilmiah Mat. Stat. Dan Terapannya (Bimaster), 4(3), 259–268.Lahallo, A. P. T. P., Widana, I. N., & Nilakusmawati, D. P. E. (2013). Perumusan Premi Bulanan Asuransi KesehatanIndividu Perawatan Rumah Sakit (Anuitas Hidup Pembayaran Bulanan). E-Jurnal Matematika, 2(4), 40–45.Munadi, & Sunarsih. (2009). Asuransi Kesehatan Kumpulan untuk Perawatan Rumah Sakit. Jurnal Matematika, 12(2),61–69.Pradipta, Y., Widana, I. N., & Sugiarto, Y. B. (2013). Pengaruh Perubahan Suku Bunga Terhadap Perhitungan Premi NetoTahunan Asuransi Kesehatan Individu. E-Jurnal Matematika, 2(3), 17–22.Qingyue, M., Liying, J., & Beibei, Y. (2011). Cost-sharing Mechanisms in Health Insurance Schemes : A systematic Review.The Alliance for Health Policy and Systems Research, WHO, 1–76.Sari, D. P., & Jazwinarti. (2016). Anuitas Last Survivor untuk Kasus Tiga Orang Tertanggung. Jurnal MIPA, 39(1), 70–77.Suryono, A. (2009). Asuransi Kesehatan Berdasarkan Undang-Undang Nomor 3 Tahun 1992. Jurnal Dinamika Hukum,9(3), 213–221.Wilandari, Y. (2007). Asuransi Kesehatan Individu Perawatan Rumah Sakit. Jurnal Matematika, 10(3), 73–78.

The Determination of Monthly Premium of Joint Term Health Insurance for Hospital Care

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The Determination of Monthly Premium of Joint Term Health Insurance for Hospital Care

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