Exercise 2: (Theory on pages \( 169-170 \) ) 1) Sarah buys a microwave for R2 500 and pays for it using a hire purchase loan. The interest rate is \( 18 \% \) per annum and the loan is to paid back over 2 years. Calculate: a) Sarah's monthly repayments. b) The interest that Sarah pays over 2 years.

To calculate Sarah's monthly repayments and the total interest paid over 2 years for her hire purchase loan, we can use the formula for the monthly payment on an installment loan, which is given by: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] Where: - \( M \) = monthly payment - \( P \) = principal amount (the loan amount) - \( r \) = monthly interest rate (annual interest rate divided by 12) - \( n \) = total number of payments (number of months) ### Given: - Principal amount \( P = R2,500 \) - Annual interest rate = \( 18\% \) or \( 0.18 \) - Monthly interest rate \( r = \frac{0.18}{12} = 0.015 \) - Loan term = 2 years = \( 2 \times 12 = 24 \) months ### a) Calculate Sarah's monthly repayments: Substituting the values into the formula: \[ M = 2500 \frac{0.015(1 + 0.015)^{24}}{(1 + 0.015)^{24} - 1} \] Calculating \( (1 + 0.015)^{24} \): \[ (1 + 0.015)^{24} \approx 1.432364654 \] Now substituting this back into the formula: \[ M = 2500 \frac{0.015 \times 1.432364654}{1.432364654 - 1} \] Calculating the numerator: \[ 0.015 \times 1.432364654 \approx 0.02148546981 \] Calculating the denominator: \[ 1.432364654 - 1 \approx 0.432364654 \] Now substituting these values: \[ M = 2500 \frac{0.02148546981}{0.432364654} \approx 2500 \times 0.0497 \approx 124.25 \] So, Sarah's monthly repayments are approximately **R124.25**. ### b) Calculate the total interest that Sarah pays over 2 years: First, we calculate the total amount paid over the 2 years: \[ \text{Total amount paid} = M \times n = 124.25 \times 24 \approx 2982 \] Now, we can find the total interest paid by subtracting the principal from the total amount paid: \[ \text{Total interest} = \text{Total amount paid} - P = 2982 - 2500 = 482 \] Thus, the total interest that Sarah pays over 2 years is approximately **R482**. ### Summary: - a) Sarah's monthly repayments: **R124.25** - b) Total interest paid over 2 years: **R482**