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.