This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright Mazindela — let's do this. 1.1 In the given context of a loan, interest is the additional money paid by the borrower to the lender for the use of the principal amount over a specified period. It represents the cost of borrowing money. 1.2 Option 2 (ABCBank) has an interest rate of 8.3% per annum. To find the interest rate per month, we divide the annual rate by 12. Monthly interest rate = (8.3\%)/(12) Monthly interest rate = (0.083)/(12) Monthly interest rate ≈ 0.0069166... Monthly interest rate = 0.69\% per month 1.3 One advantage of a fixed interest rate is that it provides predictability for the borrower, as the repayment amounts remain constant throughout the loan period, making budgeting easier. 1.4 Step 1: Identify the principal amount, interest rate, and investment period for Option 1. Principal (P) = R20 000 Interest rate (i) = 8.8% p.a. = 0.088 Investment period (n) = 2 years Compounding frequency: yearly Step 2: Use the compound interest formula to calculate the future value (A). A = P(1 + i)^n A = R20000(1 + 0.088)^2 A = R20000(1.088)^2 A = R20000 × 1.183744 A = R23674.88 1.5 To prove or disprove Nomkhosi's claim, we need to calculate the total amount payable for all three options and compare them. Option 1: JIT Bank (Calculated in 1.4) Total Repayment = R23674.88 Option 2: ABCBank Principal (P) = R20 000 Interest rate (i) = 8.3% p.a. = 0.083 Investment period (n) = 2 years Compounding frequency (m) = biannually (2 times per year) A = P(1 + (i)/(m))^n × m A = R20000(1 + (0.083)/(2))^2 × 2 A = R20000(1 + 0.0415)^4 A = R20000(1.0415)^4 A = R20000 × 1.175069... Total Repayment = R23501.38 Option 3: Parents Principal (P) = R20 000 Interest rate (i) = 9.2% p.a. = 0.092 Investment period (n) = 2 years Interest type: simple interest A = P(1 + i × n) A = R20000(1 + 0.092 × 2) A = R20000(1 + 0.184) A = R20000(1.184) Total Repayment = R23680.00 Comparison: Option 1: R23674.88 Option 2: R23501.38 Option 3: R23680.00 The lowest total repayment amount is R23501.38, which corresponds to Option 2. Therefore, Nomkhosi's statement that Option 1 will be the best is incorrect. Option 2 is the best as it results in the lowest total repayment. Send me the next one 📸