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Question: Tebogo's parents decided that since they cannot afford to cover the total cost of R 14 000 needed for the trip to Cape Town. They decided to borrow the remaining balance of R5 425 at Mbibane Bank. The bank offered them the following options. Option 1:. R 5 425 at 9.7 % per , simple interest for 2 years . Option 2: R5 425 at 9.5% per year compounded yearly for 2 years. Tebogo's father said that option 1 will be the better option. Verify with calculations if his statement is valid.

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.

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