Abusiswe loans R78 500 from a bank to buy a car. She agrees to repay the amount with interest in equal monthly instalments. The bank adds simple interest at a rate of \( 7.5 \% \) over 3 years to the amount. Calculate the following: 4.1 the total amount Abusiswe has to pay 4.2 the monthly instalments she has to pay
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To calculate the total amount Abusiswe has to pay, we first need to find the interest charged on the loan. The formula for simple interest is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] Plugging in the values: - Principal = R78,500 - Rate = 7.5% (or 0.075) - Time = 3 years \[ \text{Interest} = R78,500 \times 0.075 \times 3 = R17,662.50 \] Now, we can find the total amount: \[ \text{Total Amount} = \text{Principal} + \text{Interest} = R78,500 + R17,662.50 = R96,162.50 \] For the monthly instalments, we divide the total amount by the number of months in 3 years (which is 36 months): \[ \text{Monthly Instalment} = \frac{\text{Total Amount}}{\text{Number of Months}} = \frac{R96,162.50}{36} \approx R2,671.19 \] 4.1 The total amount Abusiswe has to pay is R96,162.50. 4.2 The monthly instalments she has to pay are approximately R2,671.19.