Question: Shanquayle Jenkins needs to calculate the effective interest rate of a simple discount note for $15,500, at an ordinary bank discount rate of 7.88%, for 120 days. Find the effective rate.
1. **State the problem:** We need to find the effective interest rate of a simple discount note with a face value of $15,500, a bank discount rate of 7.88%, and a term of 120 days.
2. **Formula used:** The effective interest rate $r$ for a simple discount note is given by:
$$r = \frac{d}{1 - d}$$
where $d$ is the bank discount rate for the period.
3. **Convert the annual discount rate to the period rate:** Since the bank discount rate is annual and the term is 120 days, we calculate the period discount rate $d$ as:
$$d = \text{annual discount rate} \times \frac{\text{days}}{360} = 0.0788 \times \frac{120}{360} = 0.0788 \times \frac{1}{3} = 0.026267$$
4. **Calculate the effective interest rate:**
$$r = \frac{0.026267}{1 - 0.026267} = \frac{0.026267}{\cancel{1} - 0.026267} = \frac{0.026267}{0.973733} \approx 0.02697$$
5. **Convert to percentage:**
$$r \approx 2.697\%$$
**Final answer:** The effective interest rate for the 120-day simple discount note is approximately **2.70%**.