1. The hire purchase price of a retrigerctor is 8.8500 . The deposit of 8500 is mode and the remainder is poid in equal monthly porments of R250. a Calculate the number of monthly payments that rust be mode b. If the cash price is R4 000 , express as a percentage of the cash price the extra cost of buying on hire putchose. c What is the interest cate (simple interest) charged on this transoctioni?

Let's break down the problem step by step. ### Known Conditions: 1. Hire purchase price of the refrigerator: \( P = 8850 \) 2. Deposit made: \( D = 8500 \) 3. Monthly payment: \( M = 250 \) 4. Cash price: \( C = 4000 \) ### Part (a): Calculate the number of monthly payments To find the number of monthly payments, we first need to determine the amount that needs to be financed after the deposit is made. 1. Calculate the financed amount: \[ F = P - D \] where \( F \) is the financed amount. 2. The number of monthly payments \( N \) can be calculated using: \[ N = \frac{F}{M} \] Let's calculate \( F \) and \( N \). ### Part (b): Express the extra cost of buying on hire purchase as a percentage of the cash price The extra cost of buying on hire purchase is given by: \[ \text{Extra Cost} = P - C \] To express this as a percentage of the cash price: \[ \text{Percentage} = \left( \frac{\text{Extra Cost}}{C} \right) \times 100 \] ### Part (c): Calculate the interest rate charged on this transaction The total amount paid through hire purchase is: \[ \text{Total Paid} = D + (M \times N) \] The interest charged can be calculated as: \[ \text{Interest} = \text{Total Paid} - C \] The interest rate can be calculated using the formula for simple interest: \[ \text{Interest Rate} = \left( \frac{\text{Interest}}{C} \right) \times \frac{100}{\text{Time in years}} \] where Time in years is \( \frac{N}{12} \). Now, let's perform the calculations for parts (a), (b), and (c). Calculate the value by following steps: - step0: Calculate: \(8850-8500\) - step1: Subtract the numbers: \(350\) Calculate or simplify the expression \( 8850 - 4000 \). Calculate the value by following steps: - step0: Calculate: \(8850-4000\) - step1: Subtract the numbers: \(4850\) Calculate or simplify the expression \( (8850 - 8500) / 250 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(8850-8500\right)}{250}\) - step1: Remove the parentheses: \(\frac{8850-8500}{250}\) - step2: Subtract the numbers: \(\frac{350}{250}\) - step3: Reduce the fraction: \(\frac{7}{5}\) Calculate or simplify the expression \( (8850 - 4000) / 4000 * 100 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(8850-4000\right)}{4000}\times 100\) - step1: Remove the parentheses: \(\frac{8850-4000}{4000}\times 100\) - step2: Subtract the numbers: \(\frac{4850}{4000}\times 100\) - step3: Reduce the fraction: \(\frac{97}{80}\times 100\) - step4: Reduce the numbers: \(\frac{97}{4}\times 5\) - step5: Multiply: \(\frac{97\times 5}{4}\) - step6: Multiply: \(\frac{485}{4}\) Calculate or simplify the expression \( 8500 + (250 * ((8850 - 8500) / 250)) - 4000 \). Calculate the value by following steps: - step0: Calculate: \(8500+\left(250\left(\frac{\left(8850-8500\right)}{250}\right)\right)-4000\) - step1: Remove the parentheses: \(8500+\left(250\left(\frac{8850-8500}{250}\right)\right)-4000\) - step2: Subtract the numbers: \(8500+\left(250\left(\frac{350}{250}\right)\right)-4000\) - step3: Reduce the fraction: \(8500+\left(250\times \frac{7}{5}\right)-4000\) - step4: Multiply the numbers: \(8500+350-4000\) - step5: Calculate: \(4850\) Calculate or simplify the expression \( ((8500 + (250 * ((8850 - 8500) / 250)) - 4000) / 4000) * (100 / ((8850 - 8500) / 250) / 12) \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{\left(8500+\left(250\left(\frac{\left(8850-8500\right)}{250}\right)\right)-4000\right)}{4000}\right)\left(\frac{\frac{100}{\left(\frac{\left(8850-8500\right)}{250}\right)}}{12}\right)\) - step1: Remove the parentheses: \(\left(\frac{8500+\left(250\left(\frac{8850-8500}{250}\right)\right)-4000}{4000}\right)\left(\frac{\frac{100}{\frac{8850-8500}{250}}}{12}\right)\) - step2: Subtract the numbers: \(\left(\frac{8500+\left(250\left(\frac{350}{250}\right)\right)-4000}{4000}\right)\left(\frac{\frac{100}{\frac{8850-8500}{250}}}{12}\right)\) - step3: Reduce the fraction: \(\left(\frac{8500+\left(250\times \frac{7}{5}\right)-4000}{4000}\right)\left(\frac{\frac{100}{\frac{8850-8500}{250}}}{12}\right)\) - step4: Multiply the numbers: \(\left(\frac{8500+350-4000}{4000}\right)\left(\frac{\frac{100}{\frac{8850-8500}{250}}}{12}\right)\) - step5: Calculate: \(\left(\frac{4850}{4000}\right)\left(\frac{\frac{100}{\frac{8850-8500}{250}}}{12}\right)\) - step6: Reduce the fraction: \(\frac{97}{80}\left(\frac{\frac{100}{\frac{8850-8500}{250}}}{12}\right)\) - step7: Subtract the numbers: \(\frac{97}{80}\left(\frac{\frac{100}{\frac{350}{250}}}{12}\right)\) - step8: Reduce the fraction: \(\frac{97}{80}\left(\frac{\frac{100}{\frac{7}{5}}}{12}\right)\) - step9: Divide the terms: \(\frac{97}{80}\left(\frac{\frac{500}{7}}{12}\right)\) - step10: Divide the terms: \(\frac{97}{80}\times \frac{125}{21}\) - step11: Reduce the numbers: \(\frac{97}{16}\times \frac{25}{21}\) - step12: Multiply the fractions: \(\frac{97\times 25}{16\times 21}\) - step13: Multiply: \(\frac{2425}{336}\) ### Part (a): Calculate the number of monthly payments 1. **Financed Amount**: \[ F = 8850 - 8500 = 350 \] 2. **Number of Monthly Payments**: \[ N = \frac{350}{250} = 1.4 \] Since the number of payments must be a whole number, we round up to the nearest whole number, which means \( N = 2 \) monthly payments. ### Part (b): Express the extra cost of buying on hire purchase as a percentage of the cash price 1. **Extra Cost**: \[ \text{Extra Cost} = 8850 - 4000 = 4850 \] 2. **Percentage of Extra Cost**: \[ \text{Percentage} = \left( \frac{4850}{4000} \right) \times 100 = 121.25\% \] ### Part (c): Calculate the interest rate charged on this transaction 1. **Total Amount Paid**: \[ \text{Total Paid} = 8500 + (250 \times 2) = 8500 + 500 = 9000 \] 2. **Interest Charged**: \[ \text{Interest} = 9000 - 4000 = 5000 \] 3. **Interest Rate Calculation**: - Time in years: \( \frac{2}{12} = \frac{1}{6} \) \[ \text{Interest Rate} = \left( \frac{5000}{4000} \right) \times \frac{100}{\frac{1}{6}} = 5000 \times \frac{100 \times 6}{4000} = 75\% \] ### Summary of Results: - **Number of Monthly Payments**: 2 - **Extra Cost as Percentage of Cash Price**: 121.25% - **Interest Rate Charged**: 75%