Calculate: \( A = 10000(1 + 0.05)^3 = 10000 \times 1.157625 = 11576.25 \).

["How to Calculate $ A = 10000(1 + 0.05)^3 $: A Simple Guide to Compound Growth", "Understanding how to calculate compounded growth is essential in finance, investing, and everyday planning. In this article, we’ll break down the calculation:", "[\nA = 10000(1 + 0.05)^3 = 10000 \ imes 1.157625 = 11576.25\n]", "### What Does the Formula Mean?", "The equation represents compound interest or growth applied over three years. Here’s what each part stands for:", "- $ A $: The final amount after interest or growth.\n- $ 10000 $: The initial principal amount (the starting value).\n- $ 1 + 0.05 $: This reflects a 5% annual rate, where 1 is the original amount and 0.05 is the decimal form of 5%.\n- $ ^3 $: The exponent means the rate is applied each year for 3 years.", "### Step-by-Step Calculation", "Let’s step through the calculation to understand how 10000 grows to 11576.25.", "1. Add the interest rate as a decimal\n [\n 1 + 0.05 = 1.05\n ]", "2. Apply the rate over 3 years using exponentiation\n Compounding annually means multiplying the initial amount by ( (1 + r)^3 ).\n [\n (1.05)^3 = 1.05 \ imes 1.05 \ imes 1.05\n ]", "First, calculate ( 1.05 \ imes 1.05 = 1.1025 ), then:\n [\n 1.1025 \ imes 1.05 = 1.157625\n ]", "3. Multiply by the principal to find the final amount\n [\n A = 10000 \ imes 1.157625 = 11576.25\n ]", "### Why This Matters", "This formula models real-world scenarios such as savings accounts, investments, and loan growth. For example, putting $10,000 into a savings account with 5% annual compound interest will yield $11,576.25 after three years.", "### Final Answer", "[\n\boxed{11576.25}\n]", "This calculation shows how a modest initial investment grows steadily through compound interest — a key concept in personal finance and long-term planning. Mastering this formula empowers smarter financial decisions every day."]