Subjects finance

Annual Interest Rate 4A7D42

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Annual Interest Rate 4A7D42


1. **State the problem:** Harry borrows 300 and pays 2.00 per day for 16 days. We need to find the annual interest rate he is effectively paying. 2. **Identify given values:** - Principal $P = 300$ - Daily interest charge $I_d = 2.00$ - Number of days $t = 16$ 3. **Calculate total interest paid:** $$I = I_d \times t = 2.00 \times 16 = 32$$ 4. **Calculate the interest rate for the 16-day period:** $$r_{16} = \frac{I}{P} = \frac{32}{300} = 0.1067 \text{ or } 10.67\%$$ 5. **Convert this to an annual interest rate:** There are approximately 365 days in a year, so the number of 16-day periods in a year is: $$n = \frac{365}{16} \approx 22.8125$$ 6. **Assuming simple interest, annual interest rate $r_{annual}$ is:** $$r_{annual} = r_{16} \times n = 0.1067 \times 22.8125 \approx 2.434$$ 7. **Convert to percentage:** $$r_{annual} = 243.4\%$$ **Answer:** Harry is paying an annual interest rate of approximately **243.4%**. This very high rate shows the cost of borrowing short-term at this daily fee.