Use the formula: \( A = P(1 + r)^n \), where \( P = 1000 \), \( r = 0.05 \), \( n = 3 \).

["# Compound Interest Formula Explained: Calculating Future Value with ( A = P(1 + r)^n )", "Understanding how investments grow over time is essential for smart financial planning. One of the most powerful tools for projecting future value is the compound interest formula:", "[\nA = P(1 + r)^n\n]", "Where:\n- ( A ) = the future value of the investment\n- ( P ) = the principal amount (initial investment)\n- ( r ) = annual interest rate (in decimal form)\n- ( n ) = number of compounding periods", "### Let’s Break It Down with Real Numbers", "Using the formula to see how money grows involves a clear set of inputs. For example, consider an investment with:", "- ( P = 1000 ) (initial principal)\n- ( r = 0.05 ) (5% annual interest rate)\n- ( n = 3 ) (compounded over 3 years)", "Plugging these into the formula gives:", "[\nA = 1000 \ imes (1 + 0.05)^3\n]", "[\nA = 1000 \ imes (1.05)^3\n]", "Now compute ( (1.05)^3 ):", "[\n1.05^3 = 1.05 \ imes 1.05 \ imes 1.05 = 1.157625\n]", "So,", "[\nA = 1000 \ imes 1.157625 = 1157.625\n]", "### Result Interpretation", "After 3 years, a $1,000 investment growing at 5% annually under annual compounding will grow to $1,157.63 (rounded to the nearest cent). This illustrates the power of compound interest — your money earns returns not just on the original amount, but on accumulated interest over time.", "### The Magic of Compounding", "What makes this formula so compelling is compounding: earning returns on past earnings. The higher ( r ) or the longer ( n ), the more exponential the growth. For long-term investors, even small annual rates can lead to substantial gains.", "### Summary", "The compound interest formula ( A = P(1 + r)^n ) is a foundational concept in personal finance. With ( P = 1000 ), ( r = 0.05 ), and ( n = 3 ), you see clearly how modest re Asper compound to meaningful growth over time. Start early — time and compound interest are your allies!", "For further planning, adjust rates or timeframes to model different scenarios:\n- What if interest doubles to 10%?\n- How long until savings reach $2,000?", "Understanding and applying ( A = P(1 + r)^n ) empowers smarter decisions with every investment."]