233. The difference between a given sum and its present worth is called its true discount.

The operation of finding the present worth of a sum of money at a fixed rate of interest is the same as the operation of finding the principal, when the amount, time, and rate per cent are given (§ 226).

Find the present worth and discount of $1000 due at the end of 3 yrs. 6 mos., at 6%.

=

The interest of $1 for 3 yrs. 6 mos., at 6%, is 3 × 6 cts.
Therefore the amount of $1 for the given time = $1.21
Hence the present worth is $1000

1.21 = $826.45.

The discount is $1000 - $826.45 = $173.55.

Ex. 149.

Find the present worth and discount of: 1. $1667.31 due in 2 yrs., at 41%.

2. $8522.66 due in 1 yr. 6 mos., at 6%.

3. $500 due in 11 mos., at 5%.
4. $1208.25 due in 7 mos., at 5%.
5. $1430.40 due in 16 mos., at 31%.
6. $1356.80 due in 1 yr. 4 mos., at 41%.
7. $1148.34 due in 2 yrs. 3 mos., at 51%.
8. $1250.26 due in 8 mos., at 73%.
9. $2120 due in 1 yr., at 6%.
10. $1456 due in 8 mos. 12 dys., at 8%.
11. $715.20 due in 1 yr. 4 mos., at 31%.
12. $5000 due in 3 yrs. 6 mos., at 6%.

COMMERCIAL DISCOUNT.

234. Price-Lists are issued by manufacturers and dealers, specifying the article manufactured and sold. These prices are subject to many and various discounts. The following bill will afford a good illustration of this discount:

New York, Aug. 18, 1885.

In the first item, $3.00 is the list price per dozen of the bolts, $24 is the gross price of the 8 dozen bolts, $10.26 is the net price. This net price is found by taking 40% from $24, which leaves $14.40 ; then taking 5% from $14.40, which leaves $13.68, and then taking 25% from $13.68, which leaves $10.26.

In the second item, the gross price is $24.75. The means a discount of of the gross price, which leaves $8.25, and the 30 means there is a discount of 30% from $8.25, which leaves $5.78.

In the third item, 40% is taken off the gross price, 5% taken from the remainder thus found, then 25% from the second remainder, and then 171% from the third remainder.

NOTE. In finding 171%, first find 10%, and then add to it for 5% and for 21%. To combine two discounts so as to form one discount, from their sum take one per cent of their product. Thus, 50% and 10% 50+ 10-555%.

=

Find the net amount of a bill of :

13. $136, discounts being 50, 10, and 5. 14. $164.50, discounts being and 30.

15. $15, discounts being 40, 5, 25, and 171.

PARTIAL PAYMENTS.

235. When settlements of accounts are made at the expiration of a year or less, it is customary to reckon interest on each item from the time it is due to the time of settlement.

And when partial payments are made and indorsed on a note that contains the words with interest, provided the note is paid in full within a year, it is usual to compute the interest on the principal, and on each of the payments to the time of settlement.

Samuel Paine buys of Edgar Smith $400 worth of goods at 30 dys. At the end of 3 mos. he pays $200, and the balance 2 mos. later. Find the balance.

The time between the end of 30 dys. and the time of settlement is 4 mos. Therefore interest is reckoned on the $400 for 4 mos., and on the $200 for 2 mos.

$400+4 mos. interest = $408

$200+ 2 mos. interest = 202

Therefore balance due is

$206

A man holds a note for $1000, dated Jan. 1, 1885, on which are indorsed payments as follows: March 1, 1885, $100; Oct. 1, 1885, $50; Nov. 1, 1885, $800. What is due Jan. 1, 1886, interest at 6% ?

Amount of $1000 for 1 yr., at 6%, is
Amount of $100 for 10 mos., at 6% = $105.00

$1060.00

Amount of $50 for 3 mos., at 6%

50.75

This method is in accordance with what is called the

Merchants' Rule.

Ex. 150.

1. A note for $3000, dated April 1, 1884, payable on demand, with interest at 7%, bears the following indorsements: May 6, $600; July 5, $676.11; Oct. 18, $966. What is due Jan. 1, 1885?

2. A note for $1237.50, dated April 17, 1884, payable on demand, bears the following indorsements: June 5, $253; Aug. 20, $274.50; Nov. 17, $420. What is due Jan. 1, 1885, reckoning interest at 6% ?

3. A note for $775.50, dated May 15, 1884, payable on demand, bears the following indorsements: July 21, $150; Oct. 10, $250; Feb. 24, 1885, $100. What is due May 15, 1885, reckoning interest at 6%? 4. A note for $1670.50, dated July 1, 1884, payable on demand, with interest at 61%, bears the following indorsements: Aug. 20, $315; Sept. 21, $360.50; Oct. 5, $400; Dec. 1, $160. What is due Jan. 1, 1885?

236. When a note that contains the words "with interest" runs longer than a year, and partial payments have been made, the interest is computed by a rule adopted by the Supreme Court of the United States, and therefore called

THE UNITED STATES RULE.

Find the amount of the principal to the time when the payment, or sum of the payments, equals or exceeds the interest.

From this amount deduct the payment or sum of the pay

ments.

Consider the remainder as a new principal, and proceed as before.

Ex. A note of $1520, dated May 20, 1884, and drawing interest at 6%, had payments indorsed upon it as follows: Oct. 2, 1884, $300; Feb. 26, 1885, $25; April 2, 1885, $570; Aug. 8, 1885, $600. Find the amount due Dec. 6, 1885.

In the first place, find the difference in time between each pair of consecutive dates. At the right of the result in each case put the corresponding decimal multiplier for the interest at 6%, and put the corresponding payment below.