Subjects finance

Loan Interest Affa98

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1. **Problem statement:** Quennie Company borrowed 500000 for 120 days at an annual interest rate of 6%, assuming a 360-day year. We need to find the total interest expense and the effective annual rate. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is interest, $P$ is principal, $r$ is annual interest rate (in decimal), and $t$ is time in years. 3. **Calculate time in years:** $$t = \frac{120}{360} = \frac{1}{3}$$ 4. **Calculate total interest expense:** $$I = 500000 \times 0.06 \times \frac{1}{3}$$ $$I = 500000 \times 0.02 = 10000$$ 5. **Effective annual rate (EAR) formula:** $$EAR = \left(1 + \frac{r \times t}{1}\right)^{\frac{1}{t}} - 1$$ 6. **Calculate EAR:** $$EAR = \left(1 + 0.06 \times \frac{1}{3}\right)^{3} - 1$$ $$EAR = \left(1 + 0.02\right)^{3} - 1 = 1.061208 - 1 = 0.061208$$ 7. **Convert EAR to percentage:** $$EAR = 6.12\%$$ **Final answers:** - Total interest expense = 10000 - Effective annual rate = 6.12%