Find the balance due on the maturity date of the note. Find the total amount of interest paid on the note. Use the United States Rule.
-Principal: $38,400
Interest: 9.2%
Time (days): 180
Partial payment: $20,000 on day 100

Question

Quizplus · Accepted Answer

To solve the problem using the United States Rule, we need to divide the time into three periods:

Period 1: From day 1 to day 100 (partial payment made)
Period 2: From day 101 to day 180 (remaining time after partial payment)
Period 3: From day 1 to day 180 (entire time)

Period 1: 
Principal = $38,400 
Rate = 9.2% 
Time = 100/360 (using a 360-day year) 
Interest = Principal x Rate x Time = $8,364.44

Since a partial payment of $20,000 was made on day 100, the outstanding principal at the beginning of Period 2 is:

Outstanding Principal = Principal - Partial Payment = $38,400 - $20,000 = $18,400

Period 2: 
Principal = $18,400 
Rate = 9.2% 
Time = 80/360 
Interest = Principal x Rate x Time = $3,413.13

Period 3: 
Total Interest = Interest from Period 1 + Interest from Period 2 = $8,364.44 + $3,413.13 = $11,777.57

Balance Due = Outstanding Principal + Total Interest = $18,400 + $11,777.57 = $19,777.57

Therefore, the answer is C) $19,777.57; $1377.57, since it is the only option that matches both the balance due and the total interest paid. Using the United States Rule, we first calculate the interest on the entire principal for 180 days:

Interest = Principal x Rate x Time
Interest = $38,400 x 0.092 x 180/360
Interest = $1,456.64

Next, we calculate the interest on the remaining balance after the partial payment:

Remaining balance = $38,400 - $20,000 = $18,400

Interest on remaining balance = $18,400 x 0.092 x 80/360
Interest on remaining balance = $411.93

Total interest paid = $1,456.64 + $411.93 = $1,868.57

Finally, we calculate the balance due on the maturity date:

Balance due = Principal - Partial payment + Interest on remaining balance
Balance due = $38,400 - $20,000 + $411.93
Balance due = $19,811.93

Therefore, the best choice is C as it correctly gives the balance due and total interest paid.

Find the Balance Due on the Maturity Date of the Note