On October 16 , the owner of a company borrowed $$ \$ 66,000 $$ on an 180 -day promissory note at $$ 9.5 \% $$ interest. Find the due date and the maturity value of the note. The due date is $$ \square / \square $$. The maturity value is $$ \$ \square $$.

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1. **Determine the interest:**

The interest rate is $$ 9.5\% $$ per year and the note is for 180 days. In many promissory note problems, it is assumed that a year has 360 days. Thus, the time in years is
   $$
   t = \frac{180}{360} = 0.5.
   $$
   
   The interest $$ I $$ is calculated using the simple interest formula:
   $$
   I = P \times r \times t,
   $$
   where $$ P = \$66,\!000 $$ and $$ r = 0.095 $$. Therefore,
   $$
   I = \$66,\!000 \times 0.095 \times 0.5 = \$66,\!000 \times 0.0475 = \$3,\!135.
   $$

2. **Calculate the maturity value:**

The maturity value is the sum of the principal and the interest:
   $$
   \text{Maturity Value} = \$66,\!000 + \$3,\!135 = \$69,\!135.
   $$

3. **Determine the due date:**

The note is issued on October 16. To find the due date, we add 180 days to October 16.
   
   - Days remaining in October from the 16th: $$ 31 - 16 = 15 $$ days.
   - Subtracting these, there are $$ 180 - 15 = 165 $$ days remaining.
   
   Now, add the days month‐by‐month:
   
   - **November (30 days):** $$ 165 - 30 = 135 $$ days remain.
   - **December (31 days):** $$ 135 - 31 = 104 $$ days remain.
   - **January (31 days):** $$ 104 - 31 = 73 $$ days remain.
   - **February (28 days):** $$ 73 - 28 = 45 $$ days remain *(assuming a non–leap year)*.
   - **March (31 days):** $$ 45 - 31 = 14 $$ days remain.
   - **April:** The remaining 14 days in April lead us to April 14.
   
   Therefore, the due date is April 14 of the following year.

4. **Final Answer:**

- The due date is $$ 04/14 $$.
   - The maturity value is $$ \$69,\!135 $$.
The due date is April 14, and the maturity value is \$69,135.

On October 16 , the owner of a company borrowed \( \$ 66,000 \) on an 180 -day promissory note at \( 9.5 \% \) interest. Find the due date and the maturity value of the note. The due date is \( \square / \square \). The maturity value is \( \$ \square \).

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