A loan is made on January 11 and has a due date of October 17 during a leap year. Find the exact time of the loan.
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To find the exact time of the loan, we need to calculate the number of days between **January 11** and **October 17** in a leap year. Since we know that leap years have 366 days (due to February 29), we must account for the correct number of days in each month.

### Steps:

1. **Count the days from January 11 to January 31** (leap year):
   - January has 31 days. So, from January 11 to January 31:  
   \( 31 - 11 + 1 = 21 \) days.

2. **Count the days in the full months from February to September** (leap year):
   - February (leap year): 29 days
   - March: 31 days
   - April: 30 days
   - May: 31 days
   - June: 30 days
   - July: 31 days
   - August: 31 days
   - September: 30 days

   Adding these gives:  
   \( 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 = 243 \) days.

3. **Count the days from October 1 to October 17**:  
   \( 17 \) days.

### Total time of the loan:
Now, sum all the days:
\[
21 \text{ (January)} + 243 \text{ (Feb–Sep)} + 17 \text{ (October)} = 281 \text{ days}.
\]

Thus, the exact time of the loan is **281 days**.

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Would you like any further details or have questions on the calculation?

### Related questions:
1. How would the calculation change if this wasn’t a leap year?
2. Can you explain why leap years have an extra day?
3. What is the difference between exact time and ordinary time of a loan?
4. How does the due date affect interest calculations on a loan?
5. What are some common methods for calculating interest on loans based on time?

**Tip**: Always double-check whether the year is a leap year or not when calculating time spans involving February!

A loan is made on January 11 and has a due date of October 17 during a leap year. Find the exact time of the loan.

Learn how to calculate the exact time of a loan made on January 11 with a due date of October 17 in a leap year. This problem involves calculating the number of days using leap year rules and detailed month-by-month breakdown. Suitable for Grades 5-7 students.

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