A partial payment is made on the date(s) indicated. Use the United

States Rule to determine the balance due on the note at the date of
maturity. (The Effective Date is the date the note was written.)
Assume the year is not a leap year.
P $1900, R 6%, effective date april 10, maturity date october 7, partial payment made may 30 $400, partial august 1 $500

The balance due on the note at the date of maturity is $1400.

To determine the balance due on the note at the date of maturity, we need to calculate the amount of interest for each period and subtract the partial payments made. Here are the steps:

Step 1: Calculate the time in days from the effective date to the first partial payment date (May 30).
Effective Date: April 10
Partial Payment Date: May 30
Time = (30 - 10) = 20 days

Step 2: Calculate the interest for the first period.
Principal: $1900
Rate: 6%
Time: 20/365 years (since year is not a leap year)
Interest = Principal x Rate x Time
Interest = $1900 x 0.06 x (20/365) = $19.53

Step 3: Subtract the first partial payment.
Balance after the first partial payment = $1900 - $400 = $1500

Step 4: Calculate the time in days from the first partial payment date to the second partial payment date (August 1).
First Partial Payment Date: May 30
Second Partial Payment Date: August 1
Time = (31 + 30 + 1) = 62 days

Step 5: Calculate the interest for the second period.
Principal: $1500
Rate: 6%
Time: 62/365 years
Interest = Principal x Rate x Time
Interest = $1500 x 0.06 x (62/365) = $15.87

Step 6: Subtract the second partial payment.
Balance after the second partial payment = $1500 - $500 = $1000

Step 7: Calculate the time in days from the second partial payment date to the maturity date (October 7).
Second Partial Payment Date: August 1
Maturity Date: October 7
Time = (31 + 7) = 38 days

Step 8: Calculate the interest for the third period.
Principal: $1000
Rate: 6%
Time: 38/365 years
Interest = Principal x Rate x Time
Interest = $1000 x 0.06 x (38/365) = $6.27

Step 9: Add up all the interest and subtract from the principal.
Balance due on the note at the date of maturity:
$1500 (Principal after first partial payment)
- $19.53 (Interest for the first period)
- $500 (Second partial payment)
- $15.87 (Interest for the second period)
- $1000 (Principal after second partial payment)
- $6.27 (Interest for the third period)
= $-42.67

The balance due on the note at the date of maturity is -$42.67, indicating that the loan has been fully paid off with an excess of $42.67.

To determine the balance due on the note at the maturity date using the United States Rule, we need to follow a few steps:

Step 1: Calculate the number of days from the effective date to the first partial payment date (May 30).
Since the effective date is April 10 and the partial payment is made on May 30, there are 50 days in between.

Step 2: Calculate the interest on the principal amount ($1900) for the number of days from the effective date to the first partial payment date.
To calculate the interest, we use the formula: Interest = (Principal * Rate * Time) / 365
Here, the rate is 6% (or 0.06), and the time is 50 days.
So, the interest is: (1900 * 0.06 * 50) / 365 = $15.89

Step 3: Subtract the first partial payment ($400) made on May 30 from the principal amount, and also deduct the interest calculated in Step 2.
Remaining balance after the first partial payment: $1900 - $400 - $15.89 = $1484.11

Step 4: Calculate the number of days from the first partial payment date (May 30) to the second partial payment date (August 1).
There are 63 days between these two dates.

Step 5: Calculate the interest on the remaining balance from Step 3 for the number of days from the first partial payment date to the second partial payment date.
Using the same formula: Interest = (Principal * Rate * Time) / 365
Here, the principal amount is $1484.11, the rate is 6% (or 0.06), and the time is 63 days.
So, the interest is: (1484.11 * 0.06 * 63) / 365 = $15.26

Step 6: Subtract the second partial payment ($500) made on August 1 from the remaining balance in Step 3, and also deduct the interest calculated in Step 5.
Remaining balance after the second partial payment: $1484.11 - $500 - $15.26 = $968.85

Step 7: Calculate the number of days from the second partial payment date (August 1) to the maturity date (October 7).
There are 68 days between these two dates.

Step 8: Calculate the interest on the remaining balance from Step 6 for the number of days from the second partial payment date to the maturity date.
Using the same formula: Interest = (Principal * Rate * Time) / 365
Here, the principal amount is $968.85, the rate is 6% (or 0.06), and the time is 68 days.
So, the interest is: (968.85 * 0.06 * 68) / 365 = $9.64

Step 9: Subtract the interest calculated in Step 8 from the remaining balance in Step 6 to find the balance due on the note at the maturity date.
Balance due on the maturity date: $968.85 - $9.64 = $959.21

Therefore, the balance due on the note at the maturity date (October 7) is $959.21.