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The principal accumulation value of simple and compound interest

Xudong Li, Mingxing He

The calculation of the principal accumulation value is the foundation of all financial calculations, and plays critical role in all financial activity such as investment, and financing. The theorem for calculations of the principal accumulation value of simple and compound interest is proposed. When a term is less than a period, the accumulated value of simple interest is more than that of compound interest; When a term is equal to a period, the accumulated value of simple interest is the same as that of compound interest; When a term is more than a period, the accumulated value of simple interest is less than that of compound interest, and the growth rate of the accumulated value of simple interest is less than that of compound interest. The theorem enriches the theory of interest. Finally, I strictly prove the theorem with Rolle’s Theorem.