1. **Problem 1: Amount needed to pay invoice within discount period** The invoice amount is 100000 with terms 2/10, net 30. This means a 2% discount is available if paid within 10 days. Formula for amount to pay with discount: $$\text{Amount to pay} = \text{Invoice amount} \times (1 - \text{Discount rate})$$ Calculation: $$100000 \times (1 - 0.02) = 100000 \times 0.98 = 98000$$ So, Carmen Traders needs 98000 to pay within the discount period. 2. **Problem 2: Principal amount of loan to raise needed funds** The company needs 98000 but must maintain a 10% compensating balance on the loan principal in a non-interest earning account. Let $P$ be the principal loan amount. The usable funds from the loan are: $$P - 0.10P = 0.90P$$ This must equal the needed amount 98000: $$0.90P = 98000$$ Solving for $P$: $$P = \frac{98000}{0.90}$$ Intermediate step with cancellation: $$P = \frac{98000}{\cancel{0.90}} \times \cancel{\frac{1}{0.90}} = 108888.89$$ So, the principal loan amount must be approximately 108888.89. 3. **Problem 3: Effective interest rate of the loan** The loan is a 30-day discounted interest loan at 12% per annum. Discounted interest means interest is deducted upfront. Interest amount: $$\text{Interest} = P \times r \times t$$ Where: - $P = 108888.89$ - $r = 0.12$ (annual rate) - $t = \frac{30}{360} = 0.0833$ (time in years, assuming 360-day year) Calculate interest: $$108888.89 \times 0.12 \times 0.0833 = 1088.89$$ Funds received by borrower: $$\text{Funds received} = P - \text{Interest} = 108888.89 - 1088.89 = 107800$$ Effective interest rate is interest divided by funds received, annualized: $$\text{Effective rate} = \frac{\text{Interest}}{\text{Funds received}} \times \frac{360}{30} = \frac{1088.89}{107800} \times 12 = 0.1212 = 12.12\%$$ 4. **Problem 4: Annual cost of non-free trade credit if discount not taken** If payment is made on day 30, no discount is taken, so full 100000 is paid. Cost of not taking discount is the discount lost: $$\text{Discount lost} = 100000 - 98000 = 2000$$ The credit period difference is 20 days (30 - 10). Annual cost of not taking discount: $$\text{Annual cost} = \frac{\text{Discount lost}}{\text{Amount paid after discount}} \times \frac{360}{\text{Extra days}} = \frac{2000}{98000} \times \frac{360}{20} = 0.02041 \times 18 = 0.3673 = 36.73\%$$ **Final answers:** 1. Amount needed to pay invoice within discount period: 98000 2. Principal loan amount needed: 108888.89 3. Effective interest rate of loan: 12.12% 4. Annual cost of non-free trade credit: 36.73%