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# Comparing Repayment Options for Tebogo's Father

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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)

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To determine whether Tebogo's father is correct in choosing Option 1 over Option 2, let’s calculate the total amount to be repaid for both options. ### 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 interest rate (9.7% or 0.097) - $$t$$ is the time in years (2 years) First, calculate the interest: $\text{Interest} = R5 425 \times 0.097 \times 2$ $\text{Interest} = R5 425 \times 0.194$ $\text{Interest} = R1 051.45$ Thus, the total amount to be repaid for Option 1 is: $\text{Total Amount} = P + \text{Interest}$ $\text{Total Amount} = R5 425 + R1 051.45$ $\text{Total Amount} = R6 476.45$ ### Option 2: Compound Interest Compound interest is calculated using the formula: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ 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) - $$n$$ is the number of times interest is compounded per year (1 for yearly) - $$t$$ is the time the money is invested for in years (2 years) First, calculate the amount: $A = R5 425 \left(1 + \frac{0.095}{1}\right)^{1 \times 2}$ $A = R5 425 \left(1 + 0.095\right)^2$ $A = R5 425 \left(1.095\right)^2$ $A = R5 425 \left(1.199025\right)$ $A = R6 504.21$ ### Comparison - **Option 1 Total Amount**: R6 476.45 - **Option 2 Total Amount**: R6 504.21 Based on the calculations, Option 1 requires repaying R6 476.45, while Option 2 requires repaying R6 504.21. Therefore, Tebogo's father is correct; Option 1 is indeed the better option, as it results in a lower total repayment amount.

Aug. 12, 2024, 6:49 a.m.

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