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All Journal Jurnal Riset Mahasiswa Matematika
Nabila Asyiqotur Rohmah
UIN Kiai Ageng Muhammad Besari
Mathematics

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Comparative Analysis of Pension Fund Investment Strategies: Time versus Contribution Size in Logistic Growth Model Nabila Asyiqotur Rohmah
Jurnal Riset Mahasiswa Matematika Vol 5, No 5 (2026): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i5.42173

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.
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