up 1 SA papers - Search IEB Mathematics Past Papers |: Mathematics google classroom - Search tps://classroom.google.com/c/NzQ1Mzg3NzMzMjg5 AL MATHEMATICS-Present Value.pptx Open with EXAMPLE Mandy takes out a ten-year loan of R80 000. She repays the loan by means of equal monthly payments starting four months after the granting of the loan. The interest rate is \( 12 \% \) per annum compounded monthly. Calculate the monthly payments. CHECK FOR RagernwTANoHNG

To calculate the monthly payments for Mandy's loan, we can use the formula for calculating the present value of an annuity. Given: - Loan amount: R80,000 - Interest rate: 12% per annum compounded monthly - Loan duration: 10 years - Repayment starts 4 months after the loan is granted First, we need to calculate the monthly interest rate: \[ \text{Monthly interest rate} = \frac{12\%}{12} = 1\% \] Next, we can use the formula for the present value of an annuity to calculate the monthly payment: \[ \text{Monthly payment} = \frac{\text{Loan amount} \times \text{Monthly interest rate}}{1 - (1 + \text{Monthly interest rate})^{-\text{Number of payments}}} \] Where: - Number of payments = 10 years * 12 months/year - 4 months = 116 months Let's calculate the monthly payment using the formula. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(80000\times 0.01\right)}{\left(1-\left(1+0.01\right)^{-116}\right)}\) - step1: Remove the parentheses: \(\frac{80000\times 0.01}{1-\left(1+0.01\right)^{-116}}\) - step2: Add the numbers: \(\frac{80000\times 0.01}{1-1.01^{-116}}\) - step3: Convert the expressions: \(\frac{80000\times 0.01}{1-\left(\frac{101}{100}\right)^{-116}}\) - step4: Multiply the numbers: \(\frac{800}{1-\left(\frac{101}{100}\right)^{-116}}\) - step5: Subtract the numbers: \(\frac{800}{\frac{101^{116}-100^{116}}{101^{116}}}\) - step6: Multiply by the reciprocal: \(800\times \frac{101^{116}}{101^{116}-100^{116}}\) - step7: Multiply: \(\frac{800\times 101^{116}}{101^{116}-100^{116}}\) The monthly payment for Mandy's loan is approximately R1,168.39.