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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. (8)

Let's evaluate both options using the given interest rates and time period to determine which option is better for Tebogo's parents. ### Option 1: Simple Interest For simple interest, the formula is: \[ A = P(1 + rt) \] Where: - \( A \) is the amount after time \( t \), - \( P \) is the principal amount (\( R 5 425 \)), - \( r \) is the annual interest rate (expressed as a decimal), and - \( t \) is the time in years. Given: - \( P = R 5 425 \), - \( r = 9.7\% = 0.097 \), - \( t = 2 \) years. Calculate the amount (\( A \)): \[ A = 5425 \times (1 + 0.097 \times 2) \] \[ A = 5425 \times (1 + 0.194) \] \[ A = 5425 \times 1.194 \] \[ A = 6481.45 \] So the total amount to be paid after 2 years with Option 1 is \( R 6 481.45 \). ### Option 2: Compound Interest For compound interest, the formula is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount after time \( t \), - \( P \) is the principal amount (\( R 5 425 \)), - \( r \) is the annual interest rate (expressed as a decimal), - \( n \) is the number of times the interest is compounded per year, and - \( t \) is the time in years. Given: - \( P = R 5 425 \), - \( r = 9.5\% = 0.095 \), - \( n = 1 \) (compounded yearly), - \( t = 2 \) years. Calculate the amount (\( A \)): \[ A = 5425 \left(1 + \frac{0.095}{1}\right)^{1 \times 2} \] \[ A = 5425 \left(1 + 0.095\right)^2 \] \[ A = 5425 \times (1.095)^2 \] \[ A = 5425 \times 1.199025 \] \[ A = 6502.21 \] (rounded to the nearest cent) So the total amount to be paid after 2 years with Option 2 is \( R 6 502.21 \). ### Comparison: - Option 1 (Simple Interest): \( R 6 481.45 \) - Option 2 (Compound Interest): \( R 6 502.21 \) Since \( R 6 481.45 \) (Option 1) is less than \( R 6 502.21 \) (Option 2), Tebogo's father is correct in saying that Option 1 is the better option.

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