A bank account has an initial balance of $1000 and earns 5% interest compounded annually. What is the balance after 3 years?
["Calculating Your Bank Account Growth: $1,000 at 5% Annual Compound Interest", "When you open a bank account, understanding how your money grows over time is essential. A common scenario many new savers encounter is starting with an initial balance and watching it grow through compound interest. For example, if you deposit $1,000 into a savings account earning 5% interest compounded annually, you might wonder: What will the balance be after 3 years?", "### What Is Compound Interest?", "Compound interest means that interest is calculated not just on your original deposit but also on the accumulated interest from previous periods. This “interest on interest” effect significantly boosts savings over time—especially with longer time horizons and steady compounding.", "### The Formula for Compound Interest", "The balance after n years can be calculated using the formula:", "$$\nA = P (1 + r)^n\n$$", "Where:\n- $ A $ = final balance\n- $ P $ = principal amount ($1,000 in this case)\n- $ r $ = annual interest rate (5% = 0.05)\n- $ n $ = number of years (3 years)", "### Applying the Numbers", "Plugging in the values:", "$$\nA = 1000 \ imes (1 + 0.05)^3\n$$\n$$\nA = 1000 \ imes (1.05)^3\n$$", "Calculating $ (1.05)^3 $:\n$$\n1.05 \ imes 1.05 = 1.1025,\quad 1.1025 \ imes 1.05 \approx 1.157625\n$$", "Then:\n$$\nA = 1000 \ imes 1.157625 = 1157.63\n$$", "### Final Balance After 3 Years", "After 3 years, a $1,000 deposit earning 5% annual compound interest will grow to $1,157.63.", "### Why This Matters", "This calculation highlights the powerful effect of compound interest over time. Even a modest starting amount like $1,000 can nearly double in less than four years with consistent annual compounding. This makes early saving and long-term investing smart financial habits.", "In summary: For an initial bank account balance of $1,000 earning 5% interest compounded annually, the balance after 3 years is approximately $1,157.63. Start early, stay consistent, and watch your money grow effortlessly.", "---", "Keywords: compound interest calculation, bank account interest, $1000 balance interest, 5% annual compound interest, how much is $1000 after 3 years, interest growth formula, compound interest example, financial growth calculation, interest on interest growth."]
