A certain investment grows according to the formula \( A = P(1 + r)^t \). If $10,000 is invested at an annual interest rate of 5% for 3 years, what is the total amount after 3 years?

["Understanding Compound Growth: A Simple Guide to Investment Returns Using the Formula ( A = P(1 + r)^t )", "When it comes to growing wealth through investments, one of the most powerful concepts is compound interest. Understanding how your money grows over time using the formula ( A = P(1 + r)^t ) empowers better financial decisions. Whether you’re saving for retirement, education, or long-term goals, knowing how to apply this formula can make a real difference.", "### What is the Formula for Compound Growth?", "The formula ( A = P(1 + r)^t ) defines the future value ( A ) of an investment, where:", "- ( A ) = total amount after time ( t )\n- ( P ) = principal amount (initial investment)\n- ( r ) = annual interest rate (expressed as a decimal)\n- ( t ) = number of years the money is invested", "This equation shows that your investment grows exponentially over time, with interest earning interest — a cornerstone of wealth accumulation.", "### Examples in Practice: $10,000 at 5% Over 3 Years", "Let’s apply this formula to a real-world example:", "- ( P = 10,000 ) dollars\n- ( r = 5% = 0.05 )\n- ( t = 3 ) years", "Plug these values into the formula:", "[\nA = 10,000 \ imes (1 + 0.05)^3 = 10,000 \ imes (1.05)^3\n]", "Now calculate ( (1.05)^3 ):", "[\n1.05^3 = 1.157625\n]", "So,", "[\nA = 10,000 \ imes 1.157625 = 11,576.25\n]", "### Result: Total Amount After 3 Years", "After 3 years, an initial investment of $10,000 at an annual interest rate of 5% will grow to $11,576.25.", "This striking example highlights the power of compound interest — earning returns not just on your principal, but on the accumulated interest over time.", "### Final Thoughts", "The formula ( A = P(1 + r)^t ) is a simple yet profound tool for understanding investment growth. With patient, consistent investing, even modest amounts can become significant sums over time. Start early, stay consistent, and let compound interest work in your favor.", "---", "Keywords: compound interest formula, investment growth, future value formula, how compound interest works, $10,000 investment 5% growth, $10,000 at 5% annual rate, exponential growth in investments, long-term investment returns."]