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Application of The Fackler and Full Preliminary Term Methods In Calculating n-Year Term Life Insurance Premium Reserves Miasary, Seftina Diyah; Ulna, Jihan Ramadhani Ar-Raafi’; Siswanah, Emy
Journal Focus Action of Research Mathematic (Factor M) Vol. 7 No. 1 (2024)
Publisher : IAIN Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30762/f_m.v7i11973

Abstract

Cadangan premi harus diperhitungkan dengan baik untuk meminimalisir kerugian bagi perusahaan asuransi. Metode yang digunakan dalam menentukan cadangan premi dari asuransi jiwa berjangka pada penelitian ini adalah metode Fackler dan metode Full Preliminary Term. Penelitian ini bertujuan untuk membandingkan perhitungan cadangan premi dengan kedua metode pada asuransi jiwa berjangka. Sebelum diperhitungkannya nilai cadangan, terlebih dahulu akan ditentukan besarnya nilai premi tunggal, anuitas awal, dan premi tahunan dari asuransi jiwa berjangka. Asumsi yang digunakan dalam penelitian meliputi tertanggung seorang laki-laki dan perempuan berusia 30 tahun, jangka pertanggungan 30 tahun, suku bunga sebesar 5,75%, dan santunan yang akan diberikan oleh perusahaan asuransi kepada tertanggung adalah sebesar Rp. 200.000.000. Berdasarkan hasil yang diperoleh, dengan didasarkan pada Tabel Mortalita Indonesia (TMI) 2019 diketahui bahwa nilai cadangan Fackler dan cadangan Full Preliminary Term pada produk asuransi jiwa berjangka n-tahun memberikan nilai yang tidak sama. Diperoleh bahwa cadangan Fackler memiliki nilai yang lebih besar dibandingkan dengan cadangan Full Preliminary Term. Cadangan Fackler untuk tertanggung laki-laki pada tahun pertama sebesar Rp.369.635 sedangkan cadangan Full Preliminary Term sebesar Rp.0. Sedangkan untuk peserta perempuan, cadangan Fackler diperoleh Rp. 226.182 dan untuk cadangan Full Preliminary Term diperoleh Rp.0. Hal ini dikarenakan pada cadangan Full Preliminary Term memperhitungkan biaya operasional dari perusahaan asuransi seperti biaya administrasi, komisi agen, dan biaya-biaya lain yang dibutuhkan oleh perusahaan asuransi. Sedangkan pada cadangan Fackler tidak memperhitungkan sejumlah biaya seperti yang disebutkan pada cadangan Full Preliminary Term. Premium reserves must be calculated correctly in order to minimise losses for the insurance business. The Fackler method and the Full Preliminary Term approach were used in this study to calculate premium reserves for term life insurance. The aim of this research is to compare the approaches for calculating premium reserves for term life insurance. Before determining the reserve value, the single premium, initial annuity, and yearly premium of term life insurance will be established. The research assumptions include that the insured is a man and a woman aged 30 years, that the insurance duration is 30 years, that the interest rate is 5.75%, and that the insurance firm will pay the insured IDR. 200,000,000. According to the results, based on the 2019 Indonesian Mortality Table (TMI), the value of Fackler reserves and Full Preliminary Term reserves in n-year term life insurance contracts provide distinct values. It is discovered that Fackler reserves are more valuable than Full Preliminary Term reserves. The Fackler reserve for male insureds in the first year is IDR 369,635 while the Full Preliminary Term reserve is IDR 0. Meanwhile, Fackler's reserve for female participants was IDR. 226,182, and the Full Preliminary Term reserve was Rp. 0. This is because the Full Preliminary Term reserve accounts for the insurance company's operations expenditures, such as administration fees, agent commissions, and other expenses. Meanwhile, the Fackler reserve excludes a number of charges from the Full Preliminary Term reserve
Penentuan Premi Tahunan Dan Cadangan Premi Dengan Metode New Jersey Asuransi Endowment Status Joint Life Menggunakan Suku Bunga Stokastik Miasary, Seftina Diyah; Umami, Riza Lathifatul; Siswanah, Emy
UJMC (Unisda Journal of Mathematics and Computer Science) Vol 9 No 2 (2023): Unisda Journal of Mathematics and Computer science
Publisher : Mathematics Department, Faculty of Mathematics and Sciences Unisda Lamongan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.52166/ujmc.v9i2.5953

Abstract

Joint life endowment status insurance is insurance that pays out if the participant dies during the policy participant's first death or survives until the conclusion of the insurance period. The purpose of this study is to calculate the amount of joint life endowment status life insurance premium reserves using the New Jersey technique in the CIR model with stochastic interest rates. The CIR model's stochastic interest rate value based on Bank Indonesia interest rates from 2018 to 2022 is 0,075. According to the calculations, the resulting annual premium is lower since the number of individuals who survive is greater than the number of persons who die over the insurance period. Furthermore, the size of the New Jersey premium reserve is zero in the first year and becomes closer to the compensation value as the insurance period proceeds.
Pemanfaatan Desmos untuk Pembelajaran Matematika Interaktif bagi Guru Matematika SMK di Salatiga Nisa, Lulu Choirun; Isnawati, Ayus Riana; Rachmawati, Ariska Kurnia; Miasary, Seftina Diyah
Nuansa Akademik: Jurnal Pembangunan Masyarakat Vol. 10 No. 1 (2025)
Publisher : Lembaga Dakwah dan Pembangunan Masyarakat Universitas Cokroaminoto Yogyakarta (LDPM UCY)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47200/jnajpm.v10i1.2675

Abstract

Desmos is a web-based platform that offers interactive mathematical tools, primarily a graphing calculator, to dynamically visualize mathematical concepts. Using Desmos is one solution to the challenges of teaching mathematics, which often lacks engagement and interactivity due to its abstract nature. Mathematics teachers from vocational schools across Salatiga have received training on utilizing Desmos in teaching. As a result, 85% of participants found Desmos easy to use, 80% felt that Desmos significantly aids mathematics teaching, particularly in visualizing concepts, 76% stated that the Desmos Graphing Calculator makes graph presentations in lessons more engaging, 85% agreed that the 3D features in Desmos help students grasp abstract concepts more concretely, 90% felt that Desmos Classroom facilitates real-time interaction through the online teacher dashboard, 80% noted that Desmos Classroom helps teachers assess student work, and 85% expressed their intention to use Desmos in their classroom teaching.
Application of The Fackler and Full Preliminary Term Methods In Calculating n-Year Term Life Insurance Premium Reserves Miasary, Seftina Diyah; Ulna, Jihan Ramadhani Ar-Raafi’; Siswanah, Emy
Journal Focus Action of Research Mathematic (Factor M) Vol. 7 No. 1 (2024): Vol. 7 No. 1 (2024)
Publisher : Universitas Islam Negeri (UIN) Syekh Wasil Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30762/f_m.v7i11973

Abstract

Cadangan premi harus diperhitungkan dengan baik untuk meminimalisir kerugian bagi perusahaan asuransi. Metode yang digunakan dalam menentukan cadangan premi dari asuransi jiwa berjangka pada penelitian ini adalah metode Fackler dan metode Full Preliminary Term. Penelitian ini bertujuan untuk membandingkan perhitungan cadangan premi dengan kedua metode pada asuransi jiwa berjangka. Sebelum diperhitungkannya nilai cadangan, terlebih dahulu akan ditentukan besarnya nilai premi tunggal, anuitas awal, dan premi tahunan dari asuransi jiwa berjangka. Asumsi yang digunakan dalam penelitian meliputi tertanggung seorang laki-laki dan perempuan berusia 30 tahun, jangka pertanggungan 30 tahun, suku bunga sebesar 5,75%, dan santunan yang akan diberikan oleh perusahaan asuransi kepada tertanggung adalah sebesar Rp. 200.000.000. Berdasarkan hasil yang diperoleh, dengan didasarkan pada Tabel Mortalita Indonesia (TMI) 2019 diketahui bahwa nilai cadangan Fackler dan cadangan Full Preliminary Term pada produk asuransi jiwa berjangka n-tahun memberikan nilai yang tidak sama. Diperoleh bahwa cadangan Fackler memiliki nilai yang lebih besar dibandingkan dengan cadangan Full Preliminary Term. Cadangan Fackler untuk tertanggung laki-laki pada tahun pertama sebesar Rp.369.635 sedangkan cadangan Full Preliminary Term sebesar Rp.0. Sedangkan untuk peserta perempuan, cadangan Fackler diperoleh Rp. 226.182 dan untuk cadangan Full Preliminary Term diperoleh Rp.0. Hal ini dikarenakan pada cadangan Full Preliminary Term memperhitungkan biaya operasional dari perusahaan asuransi seperti biaya administrasi, komisi agen, dan biaya-biaya lain yang dibutuhkan oleh perusahaan asuransi. Sedangkan pada cadangan Fackler tidak memperhitungkan sejumlah biaya seperti yang disebutkan pada cadangan Full Preliminary Term. Premium reserves must be calculated correctly in order to minimise losses for the insurance business. The Fackler method and the Full Preliminary Term approach were used in this study to calculate premium reserves for term life insurance. The aim of this research is to compare the approaches for calculating premium reserves for term life insurance. Before determining the reserve value, the single premium, initial annuity, and yearly premium of term life insurance will be established. The research assumptions include that the insured is a man and a woman aged 30 years, that the insurance duration is 30 years, that the interest rate is 5.75%, and that the insurance firm will pay the insured IDR. 200,000,000. According to the results, based on the 2019 Indonesian Mortality Table (TMI), the value of Fackler reserves and Full Preliminary Term reserves in n-year term life insurance contracts provide distinct values. It is discovered that Fackler reserves are more valuable than Full Preliminary Term reserves. The Fackler reserve for male insureds in the first year is IDR 369,635 while the Full Preliminary Term reserve is IDR 0. Meanwhile, Fackler's reserve for female participants was IDR. 226,182, and the Full Preliminary Term reserve was Rp. 0. This is because the Full Preliminary Term reserve accounts for the insurance company's operations expenditures, such as administration fees, agent commissions, and other expenses. Meanwhile, the Fackler reserve excludes a number of charges from the Full Preliminary Term reserve
THE UTILIZATION OF TRANSITION MATRIX IN BONUS-MALUS SCHEME FOR DETERMINING MOTOR VEHICLE INSURANCE PREMIUMS Miasary, Seftina Diyah; Isnawati, Ayus Riana; Marmu'asyifa, Hana Zhafira
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2391-2404

Abstract

Motor vehicle usage in Indonesia ranks among the highest globally, reaching approximately 141,992,573 units. The growing variety and number of automobiles contribute significantly to traffic congestion and heightened risks to public safety. Given the inherent dangers associated with motorized transportation, including auto theft and accidents, efforts to shift these risks to insurance companies have become crucial. The fundamental idea of insurance is to establish a pool in which policyholders can manage their risk, with premiums determined by the amount of risk that each participant adds to the group. Actuaries in the field of motor vehicle insurance must generate a reasonable premium rate utilizing a variety of methodologies, including the Bonus-Malus approach. The latter, a widely utilized approach, classifies policyholders based on their claims history, incentivizing safe driving. Examining the internal dynamics of the Bonus-Malus system necessitates studying mathematics, particularly algebra, and the use of linear algebra in transition matrices is critical in anticipating changes in bonus-malus rates over time. This research is a quantitative descriptive analysis that explores the implementation of the Bonus-Malus system using a transition matrix framework. It aims to investigate the collaboration of algebra and actuarial science in a real-world application of the Bonus-Malus scheme for motor vehicle insurance, focusing on the use of the transition matrix in premium computation, utilizing secondary data from PT. Jasa Raharja Kota Semarang for the years 2021–2022. The transition matrix analysis shows that Model 2 allows for smoother class transition, lowers the possibility of high-risk class recurrence, and provides more consistent premium adjustments. This demonstrates the model's ability to create a balanced incentive structure while interpreting claim trends. Furthermore, Model 2 has a greater expected value of Loimaranta efficiency than Model 1, supporting findings that added status improves Bonus-Malus system efficiency.
Penerapan Model Profit-Loss Sharing untuk Investasi Modal Kecil Miasary, Seftina Diyah
Zeta - Math Journal Vol 6 No 1 (2021): Mei
Publisher : Universitas Islam Madura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31102/zeta.2021.6.1.1-5

Abstract

Islamic finance is a financial concept based on Islamic sharia. The underlying principle of Islamic finance is the prohibition of usury, gharar and masyir. In addition to these principles, the concept of Islamic finance which is built on the basis of justice makes many people tend to choose Islamic finance rather than conventional. In this article, we will discuss the Sharia investment model with a profit-loss sharing scheme as an alternative model to replace the practice of lending money at high interest by moneylenders in traditional markets (Rentenir scheme). Both models are applied in a lending transaction between traders and investors with a share of the results in the profit-loss sharing model of 5% and interest on loan repayments for the loan sharks of 20%. Furthermore, from each model the acquisition value is calculated in the form of the optimal portion / profit ratio for each trader and investor. The results obtained indicate that the earnings obtained by traders for the Sharia model are greater than those from the Rentenir model. Furthermore, the acquisition value of investors for the Sharia model is minus and the acquisition value of investors from the Rentenir model is 25.56%. The acquisition value of investors from the Rentenir model is very high, while in the Sharia model, investors experience losses. From these two parameters it can be concluded that the Sharia model with a profit sharing scheme is a model that benefits small traders, while the Rentenir model is a model that needs to be avoided because it is detrimental to traders and also uses the concept of usury which is forbidden in Islam.