Question: What is the effective interest rate of a simple discount note for $27,100, at an ordinary bank discount rate of 14%, for 30 days?
1. **State the problem:** We need to find the effective interest rate of a simple discount note with a face value of $27100, a bank discount rate of 14%, and a term of 30 days.
2. **Formula and explanation:** The ordinary bank discount rate uses a 360-day year. The discount $D$ is calculated as:
$$D = F \times d \times \frac{t}{360}$$
where $F$ is the face value, $d$ is the discount rate, and $t$ is the time in days.
The proceeds $P$ received by the holder are:
$$P = F - D$$
The effective interest rate $r$ is the interest earned divided by the proceeds, annualized:
$$r = \frac{D}{P} \times \frac{360}{t}$$
3. **Calculate the discount $D$:**
$$D = 27100 \times 0.14 \times \frac{30}{360} = 27100 \times 0.14 \times 0.0833 = 27100 \times 0.01167 = 316.41$$
4. **Calculate the proceeds $P$:**
$$P = 27100 - 316.41 = 26783.59$$
5. **Calculate the effective interest rate $r$:**
$$r = \frac{316.41}{26783.59} \times \frac{360}{30} = \frac{316.41}{26783.59} \times 12$$
6. **Simplify the fraction:**
$$\frac{316.41}{26783.59} \approx 0.01181$$
7. **Calculate $r$:**
$$r = 0.01181 \times 12 = 0.1417 = 14.17\%$$
**Final answer:** The effective interest rate is approximately **14.17%**.