Business Mathematics Brief 12th Edition by Stanley Salzman ,Gary Clendenen, Charles Miller

Exercise 51

Find the balance due on the maturity date of the following notes. Find the total amount of interest paid on the note. Use the United States Rule. (See Examples.)
Finding the Amount Due

On August 14, Dr. Jane Ficker signed a 180-day note for $28,500 for a used x-ray machine for her dental office. The note has an interest rate of 10% compounded annually. On October 25, a payment of $8500 is made. (a) Find the balance owed on the principal after the payment. (b) If no additional payments are made, find the amount due at maturity of the loan.
SOLUTION

Finding the Interest Paid and Amount Due

On March 1, Boston Dairy signs a promissory note for $38,500 to replace some milking equipment for their Holsteins. The note is for 180 days at a rate of 10%. The dairy makes the following partial payments: $6000 on June 9 and $3500 on July 11. Find the interest paid on the note and the amount due on the due date of the note.
SOLUTION
The first partial payment is on June 9 or, using the number of days in each month, after
(30 + 30 + 31 + 9) = 100 days.

Debt on July 11 after 2nd partial payment = $33,569.44 ? $3201.60 = $ 30,367.84
The first partial payment is made after 100 days, and the second partial payment is made after an additional 32 days. Thus, the due date of the note is 180 ? 100 ? 32 = 48 days after the second partial payment.