A sum of money is invested at 5% annual interest, compounded annually. If the investment grows to $10,500 in 3 years, what was the initial amount?

["How to Calculate the Initial Investment when Compound Interest Growth is Known", "Understanding how compound interest works is essential for investors and financial planners alike. One common question is: If a sum of money is invested at 5% annual interest, compounded annually, and grows to $10,500 in 3 years, what was the original investment? This article explains the math behind this scenario and walks you through solving for the initial payment.", "### Understanding Compound Interest", "Compound interest means that not only does interest accrue on the principal amount, but also on the accumulated interest from previous periods. When interest is compounded annually, the formula to calculate the future value (FV) of an investment is:", "[ FV = P \ imes (1 + r)^n ]", "Where:", "- ( FV ) = Future Value ($10,500 in this case)\n- ( P ) = Principal — the initial amount (what we are solving for)\n- ( r ) = Annual interest rate (5% = 0.05)\n- ( n ) = Number of compounding periods (3 years)", "### Step-by-Step Calculation", "Substitute the known values into the formula:", "[ 10,500 = P \ imes (1 + 0.05)^3 ]", "First, calculate the compound factor:", "[ (1 + 0.05)^3 = 1.157625 ]", "Now plug that in:", "[ 10,500 = P \ imes 1.157625 ]", "To isolate ( P ), divide both sides by 1.157625:", "[ P = \frac{10,500}{1.157625} ]", "[ P \approx 9,071.58 ]", "### Result", "The initial investment required—compounded annually at 5% for 3 years to grow to $10,500—is approximately $9,071.58.", "### The Financial Insight", "This calculation highlights the power of compound interest. Even though $10,500 represents a 5% annual return over 3 years, the starting principal is significantly less than the final amount. This reinforces why consistent investing early can maximize long-term growth.", "### Final Answer", "The initial amount invested was approximately $9,071.58.", "Understanding this formula empowers you to plan better investments, compare growth scenarios, and leverage compound interest effectively in personal finance.", "---", "### Key SEO Tags\n- Compound interest formula\n- Future value calculation\n- Initial investment compound interest\n- How much was invested with 5% interest\n- Financial math explanation\n- Investing to $10,500 in 3 years"]