Où \( P = 1000 \), \( r = 0.05 \), \( n = 3 \). - United Radiology

["# Compound Interest Formula Explained: Calculating Future Value When ( P = 1000 ), ( r = 0.05 ), and ( n = 3 )", "Understanding how investments grow over time is essential for smart financial planning. One of the most widely used tools to estimate future value is the compound interest formula. In this article, we explore what happens when you invest ( P = $1000 ) at an annual interest rate of ( r = 5% ) compounded annually over ( n = 3 ) years.", "## The Compound Interest Formula", "The formula for compound interest is:", "[
\nF = P \left(1 + \frac{r}{n}\right)^{nt}
\n]", "Where:
\n- ( F ) = future value of the investment
\n- ( P ) = original principal amount ($1000 in this case)
\n- ( r ) = annual interest rate (decimal)
\n- ( n ) = number of times interest is compounded per year
\n- ( t ) = number of years", "---", "## Applying the Formula with Given Values", "Plug in the known values into the formula:", "- ( P = 1000 )
\n- ( r = 0.05 ) (which is 5%)
\n- ( n = 3 ) (compounded quarterly)
\n- ( t = 3 ) years", "[
\nF = 1000 \left(1 + \frac{0.05}{3}\right)^{3 \cdot 3}
\n]", "First, simplify inside the parentheses:", "[
\nF = 1000 \left(1 + 0.0166667\right)^9
\n]", "[
\nF = 1000 \left(1.0166667\right)^9
\n]", "Now calculate ( (1.0166667)^9 ):", "Using a calculator:
\n[
\n(1.0166667)^9 \approx 1.161472
\n]", "Multiply by the principal:", "[
\nF \approx 1000 \ imes 1.161472 = 1161.47
\n]", "---", "## Result", "After 3 years, your investment of $1000 at 5% annual interest compounded quarterly grows to approximately $1161.47.", "### What This Means for Investors", "- The higher the compounding frequency, the faster your money grows.
\n- Even with a modest rate like 5%, compounding quarterly significantly boosts returns.
\n- Planning financial goals with compound interest helps visualize growth potential and inform decisions on savings, loans, or investments.", "---", "## Summary", "For ( P = 1000 ), ( r = 0.05 ), and ( n = 3 ), compound interest increases your investment from $1000 to about $1161.47 over 3 years. This powerful financial concept underlines the benefits of starting early and compounding often.", "---", "For further finance insights, explore strategies on compound interest, savings accounts, and investment planning at [your finance blog URL]."]