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

Abstract

Pension fund planning requires strategies that balance contribution size, rate of return, and investment horizon to ensure long-term financial sustainability. This study compares early investing with small sustained contributions against late investing with large short-term contributions, using a logistic growth model $\frac{dA}{dt} = r_m A\!\left(1 - \frac{A}{K}\right) + C$ solved numerically via the 4th-order Runge-Kutta method. Seven scenarios across three categories (a core comparison, a robustness check, and a trade-off analysis) were designed with total contributions held equal at Rp360,000,000 to isolate the effect of investment timing. In the core comparison, early investing at 6\% over 30 years yields Rp1,009,377,036 (total return multiplier 2.80x) versus Rp583,741,686 (1.62x) for late investing over 15 years, a 73\% difference despite identical capital outlay. More critically, in the trade-off analysis, an early strategy at 5\% over 30 years still outperformed a very late strategy at 8\% over 10 years (Rp835,280,623 versus Rp551,414,017), confirming that even a three-percentage-point return advantage cannot compensate for a shorter horizon. These findings, consistent across different return rates and validated against the classical exponential-annuity benchmark, establish investment horizon as the dominant variable in long-term accumulation and offer practical guidance for early pension fund decision-making.