This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given values and the formula for compound interest. The principal amount (P) is GH₵ 10,000. The annual interest rate (r) is 12%, which is 0.12 in decimal form. The interest is compounded monthly, so the number of times interest is compounded per year (n) is 12. The time period (t) is 10 months, which is (10)/(12) years. The formula for the total amount (A) with compound interest is: A = P(1 + (r)/(n))^nt The compound interest (CI) is then CI = A - P. Step 2: Calculate the monthly interest rate and the total number of compounding periods. The monthly interest rate is (r)/(n) = (0.12)/(12) = 0.01. The total number of compounding periods is nt = 12 × (10)/(12) = 10. Step 3: Calculate the total amount (A). Substitute the values into the formula: A = 10000(1 + 0.01)^10 A = 10000(1.01)^10 A = 10000 × 1.10462212541 A ≈ 11046.22 Step 4: Calculate the compound interest (CI). Subtract the principal from the total amount: CI = A - P CI = 11046.22 - 10000 CI = 1046.22 The compound interest is GH₵ 1046.22. Send me the next one 📸