3. Guylain borrows R15 000 from his friend, Molefe, to finish an order for his customers. Molefe offers following two options of repayment after one year: Option A: The loan plus \( 12 \% \) p.a. interest compounded half-yearly. Option B: The loan plus \( 12 \% \) simple interest p.a: 3.1 Calculate the amount Guylain has to repay according to Option A. 3.2 Calculate the amount Guylain has to repay according to Option B. 3.3 Which of the two options would Guylain prefer? Why? 3.4 Which of the two options would Molefe prefer? Why?

**3.1 Calculation according to Option A (Compound Interest Compounded Half‐Yearly)** Guylain borrows \( P = 15000 \). The annual nominal rate is \( 12\% \), but since interest is compounded half-yearly, the interest rate per half-year is \[ r = \frac{12\%}{2} = 6\% = 0.06. \] There are \( n = 2 \) compounding periods in one year. The compound interest formula is \[ A = P(1+r)^n. \] Substitute the given values: \[ A = 15000(1+0.06)^2 = 15000(1.06)^2. \] Since \[ (1.06)^2 = 1.1236, \] we have \[ A = 15000 \times 1.1236 = 16854. \] So, according to Option A, Guylain has to repay **R16854**. --- **3.2 Calculation according to Option B (Simple Interest)** For simple interest, the formula is \[ A = P(1+rt), \] where \( P = 15000 \), \( r = 0.12 \) (annual interest rate), and \( t = 1 \) year. Substituting the values: \[ A = 15000(1+0.12) = 15000 \times 1.12 = 16800. \] Thus, according to Option B, Guylain has to repay **R16800**. --- **3.3 Which Option Would Guylain Prefer and Why?** Guylain would prefer the option where he repays the least amount of money. Comparing the total amounts: - Option A: R16854 - Option B: R16800 Since \( R16800 < R16854 \), Guylain would prefer **Option B (Simple Interest)** because he ends up repaying less. --- **3.4 Which Option Would Molefe Prefer and Why?** Molefe, as the lender, would prefer the option that gives him the higher amount in repayment. Comparing the amounts: - Option A: R16854 - Option B: R16800 Because \( R16854 > R16800 \), Molefe would prefer **Option A (Compound Interest)** as it results in a higher repayment amount.