A sum of $5,000 is invested at an annual interest rate of 5%, compounded annually. What will be the amount after 4 years?
["How to Calculate Compound Interest: What Happens When $5,000 Grows at 5% Annually Over 4 Years?", "Investing money is one of the most effective ways to build wealth over time — especially when interest compounds annually. If you’ve invested a sum of $5,000 at a reliable 5% annual interest rate, understanding how much it will grow after 4 years is essential for sound financial planning. This article walks you through the calculation using the compound interest formula and explains the impact of annual compounding.", "---", "### What Is Compound Interest?", "Compound interest means that interest is calculated not only on the original principal but also on the accumulated interest from prior periods. Unlike simple interest, which only earns interest on the initial investment, compound interest allows your money to grow faster over time — a principle that rewards long-term investors.", "---", "### The Formula for Compound Interest", "The standard formula for compound interest is:", "[\nA = P \left(1 + \frac{r}{n}\right)^{nt}\n]", "Where:\n- ( A ) = the future value of the investment/loan, including interest\n- ( P ) = the principal amount ($5,000 in this case)\n- ( r ) = annual interest rate (expressed as a decimal, so 5% = 0.05)\n- ( n ) = number of times interest is compounded per year (1 for annual compounding)\n- ( t ) = number of years the money is invested (4 years)", "---", "### Step-by-Step Calculation", "Given:\n- ( P = $5,000 )\n- ( r = 0.05 )\n- ( n = 1 ) (compounded annually)\n- ( t = 4 )", "Plug values into the formula:", "[\nA = 5000 \left(1 + \frac{0.05}{1}\right)^{1 \ imes 4}\n]\n[\nA = 5000 \left(1 + 0.05\right)^4\n]\n[\nA = 5000 \ imes (1.05)^4\n]", "Now calculate ( (1.05)^4 ):", "[\n1.05^4 = 1.21550625\n]", "Then multiply by 5000:", "[\nA = 5000 \ imes 1.21550625 = 6077.53\n]", "---", "### Final Result", "After 4 years, your initial investment of $5,000, earning 5% interest compounded annually, will grow to approximately:", "$6,077.53", "---", "### Why Annual Compounding Matters", "Using annual compounding means interest is added once per year, and future earnings begin earning interest only at that annual rate. Had the interest been compounded more frequently — say quarterly — the final amount would be slightly higher. But with annual compounding, $5,000 becomes $6,077.53 in four years — a clear demonstration of the power of time and consistent reinvestment.", "---", "### Planning Your Future with Compound Interest", "This calculation highlights the exponential growth potential of compound interest. Whether you’re saving for retirement, a major purchase, or a financial goal, starting early and leveraging compound growth can significantly boost your returns. Consider automating savings and reinvesting interest to maximize long-term growth.", "---", "Summary:\n- Principal: $5,000\n- Interest Rate: 5% per year\n- Compounded Annually for 4 years\n- Future Value: $6,077.53", "Start investing today — even small amounts grow robustly with time thanks to compound interest.", "---", "Keywords: compound interest formula, calculate compound interest, $5,000 investment, annual compounding, future value calculation, 5% interest growth, 4-year investment return, compound interest impact, financial growth, long-term investing."]
