Modeling Compound Interest

Discrete Math · Axiom Academy

EXAMPLE Modeling Compound Interest Derive and analyze recurrence relations for savings accounts with regular deposits. Excellent work! You've successfully modeled compound interest using recurrence relations. Here's what we learned: First-Order Linear Non-Homogeneous: This recurrence has the form A n = c·A n-1 + d, where c is the growth factor (1 + interest rate) and d is the constant term (regular deposit). Two Components: The homogeneous part (1.005·A n-1 ) models exponential growth from interest, while the non-homogeneous part (+200) adds the constant deposit. Building Relationships: Each month's balance depends only on the previous month (first-order), with a linear relationship and an additional constant. Real-World Applications: This model applies to savings accounts, loan payments, population growth with immigration, and many other discrete-time processes. Initial Conditions Matter: The starting value A 0 = 1000 determines the entire sequence of future balances. This recurrence relation framework is fundamental to discrete mathematics and helps us understand how systems evolve over time with both multiplicative and additive changes!

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