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Exercise XLIII

Find the compound interest on: 1. $500 for 4 years at 5%, payable annually. 2. $1700 for 2 years at 4%, payable semi-annually. 3. $450 for 5 yrs., 4 mos., at 6%, payable semi-annually.

Find the compound amount on: 4. $800 for 2 years at 6%, compounded semi-annually.

5. $1848 for 5 years, 4 months, 15 days, at 7%, compounded annually.

6. Find the difference between the simple and the compound interest on $180 for 2 years at 8%, if the interest is compounded quarterly.

7. What principal will amount to $763.205 in 2 years, 9 months, at 6%, compounded annually ?

8. Find the compound interest on $500 for 3 years, 2 months, at 6%, compounded annually.

SOLUTION: By referring to the table (page 172), it will be seen that the amount of $1 for 3 yr. at 6% $1.191016.

Computing the interest on this amount for 2 mo., the amount of $1 for 3 yr. 2 mo. is $1.202926. Therefore, the amount of $500 = 500 x $1.202926 = $601.463. $601.463 – $500 = $101.463, compound interest.

Making use of the table, find the compound interest on:

9. $535 for 3 yr. 5 mo. at 7%. 10. $750.80 for 6 yr. 7 mo. at 6%. 11. $672.28 for 2 yr. 3 mo. 18 da. at 6%.

12. What rate per cent per annum, compounded semiannually, is equivalent to 44%, compounded annually?

V. PARTIAL PAYMENTS

353. A partial payment is a payment of part of a debt.

Payment on a note, or other interest-bearing obligation, is frequently made before it is due, to lessen the interest.

354. A note, or promissory note, is a written promise to pay a specified sum at a specified time, or on demand.

355. The maker, or drawer, or promisor, of a note is the person who signs it, and who thereby promises to pay it.

356. The payee is the person to whom, or to whose order, the note is made payable.

357. The face is the sum specified in the note.

Henry Sider

$ 600

Dallas, Texaderfuly 24 1904 One year

aftedalvel promisestopayto the ordeut

Abe Doe lix hundred and

Dollars at Die Eiset llational Bank Valu received da_46_Que faby uz80s.

Sikes. In this promissory note, Henry Sikes is the maker, Abe Doe the payee, $600 the face, and the face plus the interest the maturity value.

358. A negotiable note is one made payable to bearer, or to the order of the payee.

A negotiable note may be sold by the payee, the transfer being indicated by the payee's indorsing the note; that is, by writing his name across the back of the note.

By indorsing the note, the payee becomes responsible for its

payment in case the maker does not pay it. The indorser, however, may be released by first writing the words “without recourse” across the back, and then his name.

359. If a note reads “with interest,” but does not specify the rate, it draws the legal rate. If it does not call for interest, it draws none until it becomes due and payment is demanded, after which it draws the legal rate.

360. A protest is a formal declaration in writing, made by a notary public, at the request of the holder of a note, notifying the maker and the indorsers of its non-payment.

NOTE.—The failure to protest a note on the day of maturity or immediately thereafter releases the indorsers from all obligation to pay it, unless the note contains the words "protest waived."

361. The United States Rule is most generally used in making computations involving partial payments. This rule was first announced by Chancellor Kent of New York. It has been adopted by the Supreme Court of the United States, and by the courts of nearly all the states.

UNITED STATES RULE.—1. Find the amount of the given principal to the time of the first payment, and if this payment equals or exceeds the interest then due, subtract it from the amount obtained, and treat the remainder as a new principal.

2. But if the interest is greater than any payment, find the amount on the same principal to a time when the sum of the payments equals or exceeds the interest then due; subtract the sum of the payments from that amount, regard the remainder as a new principal, and proceed as before. 362. Fundamental principles of the U. S. Rule: 1. Making a payment makes the interest on the prin

cipal fall due, up to that time.

2. A partial payment must be applied first to the dis

charge of the interest due, and then the balance,

if any, to the discharge of the principal.
3. Interest must not bear interest.
4. Payments must not bear interest.

EXAMPLE

A note of $800 is dated Oct. 1, 1904, with interest at 8%. This note has the following indorsements:

Jan. 1, 1905, $80; April 19, 1905, $10; Sept. 1, 1905, $240; what was due Jan. 1, 1906?

Dates. 1906 - 1 1

NOTE.—Beginning with the latest 1905 9 1

date above, arrange the dates in order. 1905-4-19

Beginning below, subtract each date 1905— 1-1

from the one immediately above it. 1904-10 1 Payments.

3- 0.... $80.
3—18. $10.
4–12.... $240.
4-0

SOLUTION:
1. Int. on $800 for 3 mo. at 8% $16.
2. $800 + $16 $80 $736, 2d, or new principal.
3. Int. on $736 for 3 mo. 18 days at 8% $17.66.
4. $17.66 – $10 = $7.66, unpaid interest.
5. Int. on $736 for 4 mo. 12 da. at 8% = $21.59.
6. $736 + $7.66 + $21.59 – $240 = $525.25, 3d principal.
7. Int. on $525.25 for 4 mo. at 8% $14.01.
8. $525.25 + $14.01 $539.26, am't due at settlement.

REMARK.—The work may be shortened by putting steps (3) and (5) together. Since the payment ($10) is not sufficient to

discharge the interest up to that date, we should find the interest on $736 for 8 mo., which is $39.25. The am't is $736 + $39.25 $775.25. $10 + $240 $250, am't of the payments. $775.25 $250 = $525.25, 3d principal in step (6)

,

363. Business men often settle notes and accounts running for a year or less, upon which partial payments have been made, by the Mercantile Rule.

RULE.-If the time does not exceed one year, subtract the sum of the amounts of the payments to the day of settlement from the amount of the principal to the day of settlement.

If the time exceeds a year, find the balance due at the end of each year by the rule above stated, and treat it as a new principal.

NOTE.-In applying this rule, since the time is usually short (generally less than a year), it is customary to find exact interest (see Sec. 344, p. 162).

EXAMPLE

A note of $500, dated June 1, 1903, interest at 6%, had the following indorsements:

Aug. 1, 1903, $120; Oct. 1, 1903, $100; Nov. 16, 1903, $25: what was due Dec. 28, 1903?

SOLUTION : 1. Am't of $500 from June 1 to Dec. 28 (210 da.)=....... $517.26. 2. Am't of $120 from Aug. 1 to Dec. 28 (149 da.) =$122.94 3. Am't of $100 from Oct. 1 to Dec. 28 (88 da.) =$101.45 4. Am't of $25 from Nov. 16 to Dec. 28 (42 da.) $25.17 5. Sum of amounts of payments.

249.56 6. Balance due, Dec. 28, 1903..

$267.70

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