Jerome wants to buy a computer. He can only afford to pay R 500 per month. He wants to take out a hire purchase loan over 24 months at an interest rate of \( 25 \% \) per annum. Calculate the price of the computer that he can afford to buy.

To calculate the price of the computer that Jerome can afford to buy, we need to determine the total amount he will pay over the 24 months, taking into account the interest rate. 1. **Monthly Payment**: Jerome can afford to pay R 500 per month. 2. **Loan Term**: 24 months. 3. **Interest Rate**: 25% per annum. First, we need to convert the annual interest rate to a monthly interest rate: \[ \text{Monthly Interest Rate} = \frac{25\%}{12} = \frac{0.25}{12} \approx 0.0208333 \] Next, we can use the formula for the present value of an annuity to find the total price of the computer. The formula for the present value \( PV \) of an annuity is: \[ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] Where: - \( P \) is the monthly payment (R 500), - \( r \) is the monthly interest rate (0.0208333), - \( n \) is the total number of payments (24). Substituting the values into the formula: \[ PV = 500 \times \left( \frac{1 - (1 + 0.0208333)^{-24}}{0.0208333} \right) \] Calculating \( (1 + 0.0208333)^{-24} \): \[ (1 + 0.0208333)^{-24} \approx (1.0208333)^{-24} \approx 0.6107 \] Now substituting this back into the formula: \[ PV = 500 \times \left( \frac{1 - 0.6107}{0.0208333} \right) \] Calculating \( 1 - 0.6107 \): \[ 1 - 0.6107 \approx 0.3893 \] Now substituting this value: \[ PV = 500 \times \left( \frac{0.3893}{0.0208333} \right) \approx 500 \times 18.688 \approx 9344 \] Thus, the price of the computer that Jerome can afford to buy is approximately **R 9344**.