6. Jerome wants \( t 0 \) buy a computer. He can only afford to pay R 500 per month. He wants to take out a hire purchave loan oncr 24 months at an interest rate of \( 25 \% \) per annum. Calculate the price of the computer that be 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, including interest. 1. **Monthly Payment (PMT)**: R 500 2. **Number of Months (n)**: 24 3. **Annual Interest Rate (r)**: 25% or 0.25 4. **Monthly Interest Rate (i)**: \( \frac{r}{12} = \frac{0.25}{12} \approx 0.0208333 \) The formula for the present value of an annuity (which is what Jerome's payments represent) is given by: \[ PV = PMT \times \left( \frac{1 - (1 + i)^{-n}}{i} \right) \] Where: - \( PV \) is the present value (the price of the computer), - \( PMT \) is the monthly payment, - \( i \) is the monthly interest rate, - \( n \) is the number of payments. Now, 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**.