If an investment grows according to the formula \(A = P(1 + r/n)^{nt}\), where \(P = 1000\), \(r = 0.05\), \(n = 4\), and \(t = 3\), calculate the amount \(A\) after 3 years.
["How to Calculate Compound Interest: A Step-by-Step Example Using the Formula (A = P(1 + r/n)^{nt})", "Understanding how investments grow over time is essential for smart financial planning. One of the most widely used formulas to calculate compound interest is:", "[\nA = P\left(1 + \frac{r}{n}\right)^{nt}\n]", "Where:\n- (A) = future value of the investment\n- (P) = initial principal ($1000 in this case)\n- (r) = annual interest rate (as a decimal, here 5% = 0.05)\n- (n) = number of times interest is compounded per year (quarterly → (n = 4))\n- (t) = time investment is held (3 years)", "---", "### Applying the Formula Step-by-Step", "Given:\n- (P = 1000)\n- (r = 0.05)\n- (n = 4)\n- (t = 3)", "Plug these values into the compound interest formula:", "[\nA = 1000\left(1 + \frac{0.05}{4}\right)^{4 \ imes 3}\n]", "Step 1: Divide the annual rate by compounding periods:\n[\n\frac{0.05}{4} = 0.0125\n]", "Step 2: Add 1 inside the parentheses:\n[\n1 + 0.0125 = 1.0125\n]", "Step 3: Compute the exponent:\n[\n4 \ imes 3 = 12\n]", "Step 4: Calculate the power:\n[\n1.0125^{12} \approx 1.1607545\n]", "Step 5: Multiply by the principal:\n[\nA = 1000 \ imes 1.1607545 \approx 1160.75\n]", "---", "### Final Result", "After 3 years, investing $1,000 at a 5% annual interest rate compounded quarterly yields approximately $1,160.75.", "This clear example demonstrates the powerful effect of compound interest — even small, consistent returns grow significantly over time. Use this formula:\n- To estimate investment growth\n- Compare different investment options\n- Plan long-term financial goals with precision", "Start calculating today and watch your money compound every day!", "---", "Keywords for SEO: compound interest formula, how compound interest works, A = P(1 + r/n)^(nt), investment growth calculator, future value calculation, compound interest example, financial planning formula, quarterly compounding example, 5% investment return, 3-year investment calculation"]
