1. Problem 1: Calculate the total interest expense for the loan. 2. The formula for simple interest is: $$I = P \times r \times t$$ where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. Given: - Principal $P = 500000$ - Annual rate $r = 6\% = 0.06$ - Time $t = \frac{120}{360} = \frac{1}{3}$ years (since 360-day year is assumed) 4. Substitute the values: $$I = 500000 \times 0.06 \times \frac{1}{3}$$ 5. Calculate: $$I = 500000 \times 0.06 \times 0.3333 = 10000$$ 6. So, the total interest expense is $10000$. --- 1. Problem 2: Calculate the effective annual rate (EAR). 2. The formula for EAR when interest is simple and for less than a year is: $$EAR = \left(1 + \frac{r \times t}{1}\right)^{\frac{1}{t}} - 1$$ 3. Substitute $r = 0.06$ and $t = \frac{1}{3}$: $$EAR = \left(1 + 0.06 \times \frac{1}{3}\right)^{3} - 1$$ 4. Simplify inside the parentheses: $$EAR = \left(1 + 0.02\right)^{3} - 1 = 1.02^{3} - 1$$ 5. Calculate: $$EAR = 1.061208 - 1 = 0.061208$$ 6. Convert to percentage: $$EAR = 6.12\%$$ 7. So, the effective annual rate is approximately 6.12%.