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# Comparing Total Costs of Loan Options

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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.

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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.

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

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