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
To determine the best option for Mr. Moleko, we need to calculate the total amount he would have to repay for each loan option. Option 1: Uncle's loan (Simple Interest) Step 1: Identify the given values. Principal (P) = R16 000 Interest Rate (r) = 18% per annum = 0.18 Time (t) = 5 years Step 2: Calculate the simple interest (I). The formula for simple interest is I = P × r × t. I = 16000 × 0.18 × 5 I = 16000 × 0.90 I = 14400 Step 3: Calculate the total amount to be repaid (A). The total amount is the principal plus the interest: A = P + I. A = 16000 + 14400 A = 30400 The total amount to be repaid for the uncle's loan is R 30 400. Option 2: Bank's loan (Compound Interest) Step 1: Identify the given values. Principal (P) = R16 000 Interest Rate (i) = 16% per annum = 0.16 Number of compounding periods (n) = 5 years (compounded annually) Step 2: Calculate the total amount to be repaid (A). The formula for compound interest is A = P(1 + i)^n. A = 16000(1 + 0.16)^5 A = 16000(1.16)^5 A = 16000 × 2.10034100096 A = 33605.45601536 A ≈ 33605.46 The total amount to be repaid for the bank's loan is R 33 605,46. Conclusion Step 1: Compare the total amounts for both options. Uncle's loan: R 30 400 Bank's loan: R 33 605,46 Step 2: Determine the best option. Mr. Moleko wants to borrow money, so the best option is the one that requires him to repay the least amount. Since R 30 400 is less than R 33 605,46, the uncle's loan is the better option. The option that will be best for Mr. Moleko is the uncle's loan.