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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)

To determine which loan option is better, we need to compare the total amount of money that will be owed under each option after 2 years. We'll start with calculating the total amount for each option. ### Option 1: Simple Interest The formula for simple interest is: \[ A = P(1 + rt) \] where: - \( A \) is the total amount owed - \( P \) is the principal amount (R5 425) - \( r \) is the annual interest rate (9.7% or 0.097) - \( t \) is the time in years (2 years) \[ A = 5,425(1 + 0.097 \times 2) \] \[ A = 5,425(1 + 0.194) \] \[ A = 5,425 \times 1.194 \] \[ A = 6,479.45 \] So, the total amount to be repaid under Option 1 is R6,479.45. ### Option 2: Compound Interest The formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) is the total amount owed - \( P \) is the principal amount (R5 425) - \( r \) is the annual interest rate (9.5% or 0.095) - \( n \) is the number of times the interest is compounded per year (1 in this case since it's compounded yearly) - \( t \) is the time in years (2 years) Since the interest is compounded yearly, \( n = 1 \): \[ A = 5,425 \left(1 + \frac{0.095}{1}\right)^{1 \times 2} \] \[ A = 5,425 \left(1 + 0.095\right)^{2} \] \[ A = 5,425 \left(1.095\right)^{2} \] \[ A = 5,425 \left(1.199025\right) \] \[ A = 6,504.91 \] (approximately) So, the total amount to be repaid under Option 2 is R6,504.91. ### Comparing the Options - Option 1 total repayment: R6,479.45 - Option 2 total repayment: R6,504.91 ### Conclusion Since R6,479.45 < R6,504.91, Option 1 with simple interest is indeed the cheaper option. Tebogo’s father is correct in stating that Option 1 is the better option.

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