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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

Analisis Pembayaran Pensiun Aparatur Sipil Negara di Kecamatan Manggala Kota Makassar Menggunakan Metode Projected Unit Credit Pratama, Muhammad Isbar; Lismayani, Angri
Journal of Mathematics, Computations and Statistics Vol. 7 No. 1 (2024): Volume 07 Nomor 01 (April 2024)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v7i1.2453

Abstract

Program dana pensiun adalah salah satu upaya untuk menjamin kesejahteraan pegawai yang telah mencapai usia pensiun atau tidak lagi mampu bekerja secara produktif. Penelitian ini mengkaji perhitungan kewajiban aktuaria dan iuran normal dana pensiun bagi peserta program pensiun Aparatur Sipil Negara (ASN) di Kantor Kecamatan Manggala, Kota Makassar, dengan menggunakan metode Projected Unit Credit. Perhitungan ini didasarkan pada tingkat kenaikan gaji dan penerimaan gaji setahun sebelum pensiun. Metode penelitian yang digunakan adalah studi pustaka melalui literatur dari buku dan jurnal terdahulu. Hasil penelitian menunjukkan bahwa metode Projected Unit Credit menghasilkan manfaat pensiun kumulatif tertinggi sebesar Rp 138.309.729, kewajiban aktuaria sebesar Rp 1.508.252.202, dan iuran normal sebesar Rp 47.787.374. Manfaat pensiun terendah tercatat sebesar Rp 31.103.460, kewajiban aktuaria Rp 339.179.770, dan iuran normal Rp 18.843.321. Nilai iuran normal yang lebih kecil disebabkan oleh masa kerja yang panjang, sedangkan besarnya kewajiban aktuaria dipengaruhi oleh nilai sekarang dari manfaat yang akan datang.
Simulasi Sistem Dinamik Model Matematika Kasus Kecanduan Bermain Gadget Bagi Anak Usia Dini dengan Faktor Pengawasan Orang Tua Pratama, Muhammad Isbar; Lismayani, Angri
Journal of Mathematics, Computations and Statistics Vol. 6 No. 2 (2023): Volume 06 Nomor 02 (Oktober 2023)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

This research aims to develop a mathematical model to depict the changes in the level of gadgetaddiction in early childhood of the SEAR type (Susceptible - Exposed - Addicted - Recovered). Themathematical model created is then analyzed for its stability. After the stability analysis, the model is furthersubjected to simulation using Maple 18 software. The simulation is performed three times with differentvalues of parental supervision factors, namely 0.0084, 0.5217, and 0.8214. The simulation results indicatethat the higher the level of parental supervision, the faster the cases of gadget addiction in early childhooddecline.
A Study of Social Dynamics in Early Childhood Education Using the PEARS Model as a Mathematical Approach to the Spread of Cooperative and Independent Behaviors Pratama, Muhammad Isbar; Lismayani, Angri
Journal of Mathematics, Computations and Statistics Vol. 7 No. 2 (2024): Volume 07 Nomor 02 (Oktober 2024)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v7i2.4711

Abstract

This study introduces the PEARS (Potential Adopters, Exposed, Active Adopters, Reluctant Adopters, Stable Adopters) model as a mathematical framework to analyze the spread of cooperative and independent behaviors in early childhood education (ECE) settings. Traditional qualitative methods have limitations in capturing the complexity of social dynamics within classrooms, so the PEARS model, adapted from epidemiological models, offers a fresh quantitative approach. The model categorizes children into five behavioral stages, tracking the transition from initial exposure to stable adoption. Through differential equations, the PEARS model quantifies behavioral spread and interactions, allowing the calculation of key metrics, including the basic reproduction number , which indicates the likelihood of behavior propagation within the group. Numerical simulations underscore the model's applicability in predicting behavior spread and evaluating intervention strategies, facilitating data-driven insights into enhancing positive social dynamics among young children. These findings have implications for designing pedagogical interventions aimed at fostering cooperative and independent behaviors in ECE environments.
An Analysis of Expected Return and Risk for Determining the Efficient Portfolio of Financial Firms Listed on the Indonesia Stock Exchange Pratama, Muhammad Isbar; Lismayani, Angri
Journal of Mathematics, Computations and Statistics Vol. 8 No. 1 (2025): Volume 08 Nomor 01 (April 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i1.7821

Abstract

Investors can allocate their funds in many ways, but stock investment is one of the most popular. To obtain a favorable return and minimize risk, investors must consider several factors in order to achieve optimal investment outcomes. The formation of a stock portfolio serves as a means for investors to maximize their investment performance. The objective of this study is to calculate the expected return and portfolio risk to determine the efficient portfolio among financial companies listed on the Indonesia Stock Exchange. The calculations identify three portfolio combinations as the efficient ones. Portfolio 1, with a fund proportion of 40% : 60%, yields an expected return of 0.00032 or 0.032% and a portfolio risk of 0.059 or 5.9%. Portfolio 2 has an expected return of 0.0128 or 1.28% and a portfolio risk of 0.0504 or 5.04%. Portfolio 3 yields an expected return of 0.0057 or 0.57% and a portfolio risk of 0.0667 or 6.67%. Based on these results, Portfolio 2 is identified as the efficient portfolio, as it provides the highest expected return, albeit with relatively high risk. This type of investment is typically preferred by risk-seeking investors, who are inclined toward high-risk, high-return opportunities