33. The discount on a note for 90 days at 6% is $18.75.

What is the face of the note that is discounted?

34. A dealer buys $1750 worth of goods, giving his note

on October 4, for 90 days, at 5%. of the note discounts it at 6%.

On October 10 the holder Find the proceeds.

PARTIAL PAYMENTS

127. Partial payments. If a dealer holds a note against one of his customers, and it bears interest, and partial payments are made from time to time, the amount due on the day of settlement is found in the following way:

1. Add the interest to the principal whenever the payment (or sum of the payments) equals or exceeds the interest.

2. Then deduct the payment (or payments) and continue as before.

This is the United States Rule of Partial Payments, the legal one in most states. Where other rules are legal, teachers should explain the law and require the problems solved accordingly.

128. Illustrative problem. A note for $1000, at 5%, is dated January 1, 1906. The following payments are indorsed (written across the back, as is the custom): July 1, 1906, $10; January 1, 1907, $40; July 1, 1907, $20; January 1, 1908, $130. How much is due July 1, 1908?

The interest on July 1, 1906, is $25, and the payment is $10. Hence the payment cannot be deducted. The reason is easily seen, for if we should take $1025 – $10 = $1015 as the new principal, we should be drawing interest on more than the $1000.

WRITTEN EXERCISE

1. A note for $375, at 5%, has a payment of $18.75 indorsed annually at the close of each year from its date, for 3 years. How much is due at the end of the fourth year?

2. A note for $500, at 6%, is dated January 1, 1906, and has the following partial payments indorsed: July 2, 1906, $100; January 1, 1907, $100. How much is due July 1, 1907?

3. A note for $300, at 6%, is dated April 1, 1906, and has the following partial payments indorsed: September 1, 1906, $50; February 16, 1907, $75; January 1, 1908, $100. How much is due July 1, 1908 ?

4. A note for $1800, at 5%, is dated April 16, 1906, and has the following partial payments indorsed: July 2, 1906, $500; October 1, 1906, $250; February 1, 1907, $100; May 1, 1907, $375. How much is due September 5, 1907?

5. A note for $750, at 4%, is dated June 15, 1906, and has the following partial payments indorsed: March 6, 1907, $200; September 6, 1907, $150; January 17, 1908, $250. How much is due on the day of settlement, May 14, 1908?

6. A note for $600, at 5%, is dated July 2, 1906, and has the following partial payments indorsed: January 2, 1907, $50; February 11, 1907, $75; July 8, 1907, $200; September 10, 1907, $80; November 2, 1907, $50. How much is due January 2, 1908?

7. A note for $1200, at 4%, is dated May 1, 1906, and has the following partial payments indorsed: July 2, 1906, by labor, $5; July 9, 1906, by labor, $2; September 1, 1906, $93; May 1, 1907, $450; November 1, 1907, $500. How much is due January 1, 1908?

8. A note for $750, at 6%, is dated February 2, 1907, and has the following partial payments indorsed: June 2, 1907, $150; July 17, 1907, $75; February 2, 1908, $100. How much is due August 2, 1908?

9. A note for $575, at 6%, is dated January 15, 1906, and has the following partial payments indorsed: May 7, 1906, $30; August 13, 1906, $50; December 18, 1906, $75. How much is due January 30, 1907?

10. A note for $625, at 5%, is dated November 13, 1906, and has the following partial payments indorsed: February 14, 1907, $35; April 17, 1907, $75.50; October 23, 1907, $50; March 19, 1908, $135. How much is due September 23, 1908?

11. A note for $175, at 6%, is dated December 9, 1907, and has the following partial payments indorsed: February 4, 1908, $25; May 27, 1908, $63.50; September 2, 1908, $15; February 25, 1909, $20. How much is due April 22, 1909 ?

12. A note for $675.50, at 5%, is dated August 5, 1907, and has the following partial payments indorsed: January 7, 1908, $50; August 5, 1908, $50; March 18, 1909, $35; July 15, 1909, $75; November 11, 1909, $130. How much is due January 7, 1910?

13. A man owes another $750 for a village building lot, and he gives his note at 6%, due on demand, with the understanding that he should pay part of it by labor. The note is dated April 15, 1908, and the following partial payments are indorsed: July 22, 1908, 4 days' labor @ $3; September 16, 1908, 33 days' labor @ $3; January 21, 1909, 4 hours' labor @ 50; March 11, 1909, 11 days' labor @ $3; July 15, 1909, 37 days' labor @ $3; September 16, 1909, cash, $350. How much is due January 1, 1910?

129. Merchants' rule. Where a note or account runs a year or less, and partial payments have been made, business men often compute the balance due by means of a rule sometimes called The Merchants' Rule, as follows:

1. Find the amount of the principal at the time of settle

ment.

2. Find the amount of each payment from the time it was made until the time of settlement.

3. From the amount of the principal subtract the amount of the payments.

The rule, not being as fair for longer periods as the United States Rule, is not legal. But for short periods it is easier and gives nearly the same result.

130. Illustrative problem. A note for $100 made January 1 has the following payments indorsed: March 1, $10; April 1, $25. Find the balance July 1, allowing 6% interest. Amount of $100 for 6 mo.

$103

Notes for the following amounts have indorsed the payments indicated. Find the balance at the date of settlement, using the Merchants' rule, and allowing 6% interest: 1. $875, April 1. Indorsements: $300, May 1; $125, June 15; $275, July 25. Settled November 20.

2. $250, February 1. Indorsements: $30, March 1; $70, May 15; $50, July 10. Settled September 15.

3. $750, March 1. Indorsements: May 10, $100; July 12, $75; September 4, $40. Settled October 15.