Analisis Perbandingan Model Diskrit dan Kontinu dalam Prediksi Biaya Hidup Mahasiswa Selama Masa Studi

Abstract

This study aims to compare the results of student living cost estimates over a four-year study period using two approaches in financial mathematics, namely the discrete model and the continuous model. The background of the study is based on the need for students to manage their personal finances effectively amidst rising living costs due to inflation. The discrete model is used to predict expenses at certain time intervals, while the continuous model assumes that changes in the value of money occur continuously at all times. This study uses a quantitative descriptive-comparative method with controlled simulations on 100 student data with variations in monthly living costs between Rp2,000,000–Rp4,000,000 and a random inflation rate of 0%–20%. The data were analyzed using discrete and continuous growth formulas, then a Paired Sample t-Test was performed to determine significant differences between the two models. The results show that both models produce very similar living cost estimates with an average difference of only about 1–3% of the total four-year costs. The continuous model produces slightly higher results than the discrete model due to its exponential and continuous nature of calculations. However, the statistical test results showed a p-value > 0.05, indicating no statistically significant difference between the two. Practically, both approaches can be used equally in student financial planning, with the discrete model being more appropriate for short-term projections and the continuous model being more appropriate for long-term projections.