Comparative Analysis of Pension Fund Investment Strategies: Time versus Contribution Size in Logistic Growth Model

Nabila Asyiqotur Rohmah

Abstract


Pension fund planning requires optimal investment strategies to ensure financialsustainability during retirement. This study compares two common strategies,early investing with small long-term contributions versus late investing with largeshort-term contributions, using a logistic growth model $\frac{dA}{dt} = rA(1-\frac{A}{K}) + C$ solved numerically via the 4th-order Runge-Kutta method. Sevenscenarios are designed across three categories: Core Comparison (early-6\% vslate-6\%), Robustness (early-7\% vs late-7\%), and Trade-off Analysis (early-5\%vs late-6\% vs very late-8\%), all with equal total contributions ofRp360,000,000. Results show that early investing yields Rp1,009,377,036(efficiency ratio 2.80x) versus Rp583,741,686 (1.62x) for late investing, a73\% difference despite identical capital outlay. Notably, even an 8\% returncannot compensate for a delayed start against a 5\% early strategy, confirmingthat the investment horizon $t$ is the dominant variable in long-term accumulationand cannot be offset by higher contributions or returns. These findings offerpractical guidance for early pension fund decision-making and contribute to theapplication of logistic growth models in financial planning contexts.

Keywords


investment strategy; logistic growth; pension fund; Runge-Kutta; time value of money

Full Text:

PDF

References


[1] M. Syafii, “Manajemen investasi pensiun membangun dana pensiun yang kokoh untuk masa depan,” 2024.

[2] G. Apriyanto, “Manajemen dana pensiun: Sebuah pendekatan penilaian kinerja modified baldrige assessment,” Media Nusa Creative, vol. 1, no. 1, pp. 1–12, 2020.

[3] S. B. Lahuri, B. A. R. Wardani, and A. A. Zuhroh, “A comprehensive literature review on time value of money and economic value of time for financial decision-making,” Ekonomica Sharia: Jurnal Pemikiran Dan Pengembangan Ekonomi Syariah, vol. 10, no. 2, pp. 305–318, 2025. doi: 10.36908/esha.v10i2.1407

[4] Z. Bodie, A. Kane, and A. J. Marcus, Investments, 12th ed. New York: McGraw-Hill, 2021.

[5] J.-P. Aubry and Y. Yin, “How do public pension plan returns compare to simple index investing?” Center for Retirement Research at Boston College, Tech. Rep. 2024-13, 2024. Available online.

[6] V. R. Institute, “How America Saves 2024: The 23rd annual Vanguard workplace retirement savings report,” Vanguard, Tech. Rep., 2024. Available online.

[7] M. M. Baldi, C. Mammana, and E. Michetti, “The κ-logistic growth model: Qualitative and quantitative dynamics,” Mathematics and Computers in Simulation, vol. 225, pp. 350–369, 2024. doi: 10.1016/j.matcom.2024.05.016

[8] A. D. Smirnov, “Sigmoidal dynamics of macro-financial leverage,” Quantitative Finance and Economics, vol. 7, no. 1, pp. 147–164, 2023. doi: 10.3934/QFE.2023007

[9] I. Gleria, S. Da Silva, L. Brenig, T. M. Rocha Filho, and A. Figueiredo, “Modified Verhulst-Solow model for long-term population and economic growths,” arXiv preprint arXiv:2308.08315, 2023.

[10] M. A. Prabowosunu, R. Y. Siregar, R. Melati, D. Hadrian, and R. R. Ronaldo, “Identifying risk-taking behavior and prudent asset allocation in pension funds in Indonesia,” Scholar Hub UI, Tech. Rep., 2025.

[11] S. Yunus, “Investment performance of DPLK in Indonesia: Evidence from 2019–2024,” Moneter: Jurnal Akuntansi dan Keuangan, vol. 3, no. 2, pp. 1–12, 2024. doi: 10.61132/moneter.v3i2.1312

[12] F. Caravelli, L. Sindoni, F. Caccioli, and C. Ududec, “Optimal growth trajectories with finite carrying capacity,” Physical Review E, vol. 94, no. 2, p. 022315, 2016. doi: 10.1103/PhysRevE.94.022315

[13] J. A. P. Cahyono and M. Yazid, “Dana pensiun syariah,” Al-Kharaj: Jurnal Ekonomi, Keuangan & Bisnis Syariah, vol. 5, no. 4, pp. 1810–1816, 2022.

[14] D. Sari, D. Wulandari, A. A. Gaffar, A. Kadir, and M. Lutfi, “Determinants of financial performance in influencing inclusivity of sharia pension fund participants in Indonesia,” Jurnal Ekonomi, Bisnis & Entrepreneurship, vol. 18, no. 1, pp. 262–282, 2024.

[15] Y. A. Futri, R. Romadoni, Y. M. R. Wardhani, A. R. Hidayat, A. N. Baiti, and M. G. A. Adha, “Analisis instrumen pasar modal terhadap pilihan berinvestasi masyarakat generasi Z: Melalui studi literatur,” Jurnal Ilmiah Manajemen Dan Akuntansi, vol. 2, no. 3, pp. 38–49, 2025. doi: 10.69714/bpt9m607

[16] M. R. F. Maulana, T. A. Hidayah, T. A. Aisyah, and T. R. Izzalqurny, “Analisis kinerja reksadana syariah di pasar modal,” in Prosiding National Seminar on Accounting, Finance, and Economics (NSAFE), vol. 2, 2022.

[17] W. M. S. Maura, “Analisis good islamic pension fund governance (GIPFG) pada dana pensiun (Dapen) Bank Riau Kepri,” M.S. thesis, Universitas Islam Negeri Sultan Syarif Kasim Riau, 2025.

[18] P. F. Verhulst, “Notice sur la loi que la population suit dans son accroissement,” Correspondance Mathématique et Physique, vol. 10, pp. 113–121, 1838.

[19] L. K. Kholisa, L. K. Azizah, and A. N. Salamah, “Perkembangan dana pensiun syariah,” Jurnal Ilmiah Ekonomi dan Manajemen, vol. 1, no. 4, pp. 344–352, 2023.

[20] O. S. Mitchell and N. L. Roussanov, “Lessons from behavioral research for retirement saving, investment, and spending: An overview,” Wharton Pension Research Council, Tech. Rep. 2024-11, 2024.

[21] H. Tanuatmodjo, N. Nugraha, D. Disman, and T. Heryana, “Behavioral bias in retirement planning: A literature review,” in Proceedings of the 8th Global Conference on Business, Management, and Entrepreneurship (GCBME 2023), 2024, pp. 61–67.

[22] V. Baulkaran, “Behavioral biases of financial planners: The case of retirement funding recommendations,” Journal of Behavioral Finance, 2024.

[23] M. Rinaldi, Metode Numerik (Revisi Kelima), 5th ed. Jakarta: Informatika, 2021.




DOI: https://doi.org/10.18860/jrmm.v5i5.42173

Refbacks

  • There are currently no refbacks.