You have a note in the amount of $10,000 at 9.5% interest running from january 5. to april 16

a. calculate the ordinary intrest.
b. calculate the exact interest.

To calculate both the ordinary interest and the exact interest, we need to determine the "time" that the note is outstanding.

The time period from January 5 to April 16 can be broken down into two parts:

1. From January 5 to March 31: This period includes 87 days (January has 31 days, February has 28 days or 29 days in a leap year, and March has 31 days).
2. From April 1 to April 16: This period is 16 days.

Now let's calculate the ordinary interest and the exact interest based on this information:

a. Calculate the Ordinary Interest:
Ordinary interest is calculated based on a 360-day year, with each month having 30 days.

To calculate the ordinary interest, we use the simple interest formula:
Interest = Principal × Rate × Time

The principal is $10,000, the rate is 9.5% (which can be expressed as 0.095), and the total time is 103 days.

Total Time = 87 days + 16 days = 103 days

Now, plug in the values into the formula to calculate the ordinary interest:
Ordinary Interest = $10,000 × 0.095 × (103/360)

b. Calculate the Exact Interest:
Exact interest is calculated based on the actual number of days in a year, taking into account leap years.

To calculate the exact interest, we use the same simple interest formula:
Interest = Principal × Rate × Time

In this case, the time is calculated as the actual number of days divided by 365 days.

Total Time = 87 days + 16 days = 103 days

Now, plug in the values into the formula to calculate the exact interest:
Exact Interest = $10,000 × 0.095 × (103/365)

By substituting the values and performing the calculations, you can find the answers for both the ordinary interest and the exact interest.