If the compound interest on a sum of money for 2 years is $400 and the principal

If the compound interest on a sum of money for 2 years is $400 and the principal is $1600, what is the rate of interest? (2023)

If the compound interest on a sum of money for 2 years is $400 and the principal is $1600, what is the rate of interest? (2023)

Step 1: Identify the given values. The compound interest (CI) is $400, the principal (P) is $1600, and the time (n) is 2 years.
Step 2: Write down the formula for compound interest: CI = P[(1 + r)^n - 1].
Step 3: Substitute the known values into the formula: 400 = 1600[(1 + r)^2 - 1].
Step 4: Simplify the equation. Divide both sides by 1600: 400 / 1600 = (1 + r)^2 - 1.
Step 5: Calculate 400 / 1600, which equals 0.25. Now the equation is: 0.25 = (1 + r)^2 - 1.
Step 6: Add 1 to both sides of the equation: 0.25 + 1 = (1 + r)^2.
Step 7: This simplifies to: 1.25 = (1 + r)^2.
Step 8: Take the square root of both sides to solve for (1 + r): √1.25 = 1 + r.
Step 9: Calculate the square root of 1.25, which is approximately 1.118. So, 1 + r = 1.118.
Step 10: Subtract 1 from both sides to find r: r = 1.118 - 1.
Step 11: This gives r = 0.118, which is 0.118 or 11.8%.
Step 12: To express it as a percentage, multiply by 100: r = 11.8%.

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