Comparing Total Costs of Loan Options

To verify whether Tebogo's father is correct, we need to calculate the total amount to be repaid for both loan options and compare them. ### Option 1: Simple Interest Simple interest is calculated using the formula: \[ \text{Simple Interest} = P \times r \times t \] where: - \( P \) is the principal amount (R5 425), - \( r \) is the annual interest rate (9.7% or 0.097), - \( t \) is the time period in years (2 years). First, calculate the interest: \[ \text{Simple Interest} = 5425 \times 0.097 \times 2 = 1052.95 \] Next, calculate the total amount to be repaid: \[ \text{Total Amount (Simple Interest)} = P + \text{Simple Interest} \] \[ = 5425 + 1052.95 \] \[ = 6477.95 \] ### Option 2: Compound Interest Compound interest is calculated using the formula: \[ A = P \times (1 + r)^t \] where: - \( A \) is the amount of money accumulated after n years, including interest, - \( P \) is the principal amount (R5 425), - \( r \) is the annual interest rate (9.5% or 0.095), - \( t \) is the number of years the money is invested or borrowed for (2 years). Calculate the total amount using compound interest: \[ A = 5425 \times (1 + 0.095)^2 \] \[ = 5425 \times (1.095)^2 \] \[ = 5425 \times 1.199025 \] \[ = 6503.88 \] ### Comparison - Total Amount (Simple Interest) = R 6 477.95 - Total Amount (Compound Interest) = R 6 503.88 Since R 6 477.95 (Simple Interest) is less than R 6 503.88 (Compound Interest), Tebogo's father is correct that Option 1 (simple interest) is the better option, as it results in a lower total repayment.