Compound Interest Basics

Business Calculus · Axiom Academy

EXAMPLE Compound Interest Basics Calculate how investments grow with periodic compounding You invest 5,000 in an account that pays 6% annual interest , compounded monthly . Find: How much will your investment be worth after 10 years? For compound interest, we use the formula: From our problem, we can identify: What is n (the periodic interest rate)? The key part of the formula is (1 + n )^ nt . Let's calculate it step by step: First: 1 + n = 1 + 0.005 = 1.005 Then: nt = 12 10 = 120 compounding periods Now we multiply by the principal: Your 5,000 grew by 4,096.98 in 10 years! Notice that simple interest at 6% would only give you 3,000 in interest ( 5,000 × 0.06 × 10). Compound interest earned you an extra 1,096.98 because interest earns interest. Let's see how compound interest compares to simple interest over time: Your Investment After 10 Years Your 5,000 nearly doubled thanks to compound interest! More compounding periods = more growth : Monthly is better than annually Time is powerful : The longer you invest, the bigger the compound effect Coming up : What if we compound infinitely often? That's continuous compounding!

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