Pregunta
upstudy study bank question image url

3. Mr Hassiem buys a computer for his business on hire purchase. The price of the computer is R8 999 and he pays a deposit of R1 500 . The simple Interest rate is 7\% p.a. Calculate his monthly instalment if the hire purchas agreement says that he must pay back the money in 3 years' time. 4. 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 followir 4.1 the total amount Abusiswe has to pay

Ask by Higgins Norton. in South Africa
Mar 13,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

**Problem 3:** - **Monthly Instalment:** R252.05 **Problem 4:** - **Total Amount to Pay:** R96,162.50

Solución

Let's solve each problem step by step. ### Problem 3: Mr. Hassiem's Computer Hire Purchase **Known Conditions:** - Price of the computer: \( P = 8999 \) - Deposit paid: \( D = 1500 \) - Simple interest rate: \( r = 7\% \) per annum - Time period: \( t = 3 \) years **Step 1: Calculate the amount financed.** The amount financed is the price of the computer minus the deposit: \[ A = P - D = 8999 - 1500 = 7499 \] **Step 2: Calculate the total interest over 3 years.** Using the formula for simple interest: \[ I = A \cdot r \cdot t \] where \( r \) is in decimal form: \[ r = \frac{7}{100} = 0.07 \] Now, substituting the values: \[ I = 7499 \cdot 0.07 \cdot 3 \] **Step 3: Calculate the total amount to be paid back.** The total amount to be paid back is the amount financed plus the interest: \[ T = A + I \] **Step 4: Calculate the monthly instalment.** The total number of months over 3 years is: \[ n = 3 \cdot 12 = 36 \] The monthly instalment \( M \) is given by: \[ M = \frac{T}{n} \] Now, let's perform the calculations. ### Problem 4: Abusiswe's Car Loan **Known Conditions:** - Loan amount: \( L = 78500 \) - Simple interest rate: \( r = 7.5\% \) per annum - Time period: \( t = 3 \) years **Step 1: Calculate the total interest over 3 years.** Using the formula for simple interest: \[ I = L \cdot r \cdot t \] where \( r \) is in decimal form: \[ r = \frac{7.5}{100} = 0.075 \] Now, substituting the values: \[ I = 78500 \cdot 0.075 \cdot 3 \] **Step 2: Calculate the total amount to be paid back.** The total amount to be paid back is the loan amount plus the interest: \[ T = L + I \] Now, let's perform the calculations for both problems. Calculate the value by following steps: - step0: Calculate: \(7499\times 0.07\times 3\) - step1: Multiply the terms: \(524.93\times 3\) - step2: Multiply the numbers: \(1574.79\) Calculate or simplify the expression \( 78500 * 0.075 * 3 \). Calculate the value by following steps: - step0: Calculate: \(78500\times 0.075\times 3\) - step1: Multiply the terms: \(5887.5\times 3\) - step2: Multiply the numbers: \(17662.5\) Calculate or simplify the expression \( 78500 + 17662.5 \). Calculate the value by following steps: - step0: Calculate: \(78500+17662.5\) - step1: Add the numbers: \(96162.5\) Calculate or simplify the expression \( 7499 + 1574.79 \). Calculate the value by following steps: - step0: Calculate: \(7499+1574.79\) - step1: Add the numbers: \(9073.79\) Calculate or simplify the expression \( 9073.79 / 36 \). Calculate the value by following steps: - step0: Calculate: \(\frac{9073.79}{36}\) - step1: Convert the expressions: \(\frac{\frac{907379}{100}}{36}\) - step2: Multiply by the reciprocal: \(\frac{907379}{100}\times \frac{1}{36}\) - step3: Multiply the fractions: \(\frac{907379}{100\times 36}\) - step4: Multiply: \(\frac{907379}{3600}\) Calculate or simplify the expression \( 96162.5 / (3 * 12) \). Calculate the value by following steps: - step0: Calculate: \(\frac{96162.5}{\left(3\times 12\right)}\) - step1: Remove the parentheses: \(\frac{96162.5}{3\times 12}\) - step2: Multiply the numbers: \(\frac{96162.5}{36}\) - step3: Convert the expressions: \(\frac{\frac{192325}{2}}{36}\) - step4: Multiply by the reciprocal: \(\frac{192325}{2}\times \frac{1}{36}\) - step5: Multiply the fractions: \(\frac{192325}{2\times 36}\) - step6: Multiply: \(\frac{192325}{72}\) ### Solution to Problem 3: Mr. Hassiem's Computer Hire Purchase 1. **Amount Financed:** \[ A = 8999 - 1500 = 7499 \] 2. **Total Interest Calculation:** \[ I = 7499 \cdot 0.07 \cdot 3 = 1574.79 \] 3. **Total Amount to be Paid Back:** \[ T = 7499 + 1574.79 = 9073.79 \] 4. **Monthly Instalment Calculation:** \[ n = 3 \cdot 12 = 36 \] \[ M = \frac{9073.79}{36} \approx 252.05 \] **Final Answer for Problem 3:** Mr. Hassiem's monthly instalment is approximately **R252.05**. --- ### Solution to Problem 4: Abusiswe's Car Loan 1. **Total Interest Calculation:** \[ I = 78500 \cdot 0.075 \cdot 3 = 17662.5 \] 2. **Total Amount to be Paid Back:** \[ T = 78500 + 17662.5 = 96162.5 \] 3. **Monthly Instalment Calculation:** \[ n = 3 \cdot 12 = 36 \] \[ M = \frac{96162.5}{36} \approx 2671.18 \] **Final Answer for Problem 4:** The total amount Abusiswe has to pay is **R96,162.50**.

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

Extra Insights

To tackle Mr. Hassiem's hire purchase, we first need to calculate the total amount financed. The cost of the computer is R8,999, and after paying a deposit of R1,500, he has R7,499 left to finance. With a simple interest rate of 7% over 3 years, the total interest amounts to R524.93. Now, Mr. Hassiem's total repayment comes to R7,499 + R524.93 = R8,023.93. Dividing this by 36 months, his monthly instalment is approximately R222.32. Now, regarding Abusiswe's car loan, first, we calculate the total interest on her loan of R78,500 at a simple interest rate of 7.5% over 3 years. This comes out to R17,588.75 in interest. Adding this to the principal, the total amount Abusiswe has to repay becomes R96,088.75. By spreading this over 36 months, her monthly repayment would be about R2,668.02, giving her a clearer direction for her budget!

preguntas relacionadas

Latest Arithmetic Questions

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad