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If $2,34 is paid for the use of $468 for 1 mo. what is the rate per cent. ?

Ans. 6 per cent. At $46,80 for the use of $520 for 2 yrs. what is it per cent. ?

Ans. 4 per cent.

TO FIND THE TIME, WHEN THE PRINCIPAL, RATE AND

INTEREST ARE KNOWN. What is the time required to gain $3,78 on $36, at 7

per cent. ?

We first find what would be the interest on that sum for one year, at 7 per cent.

This would be $2,52. As many times as this sum is contained in the interest mentioned in the sum, so much more time than one year is required.

Rule. Divide the interest given, by the interest which the principal would gain at the same rate, in one year.

Paid $20 for the use of 600 at 8 per cent. ; what was the time?

Ans. 5 mo. Paid $28,242 for the use of $217,25 at 4 per cent. ; what was the time?

Ans. 3 yrs. 3 mo.

ENDORSEMENTS. In transacting business, it is often necessary to calculate 'interest upon notes, where partial payments have been made, and endorsed upon the note. For example, a man borrows $500, and gives his note, promising to repay it with interest.

Two years after, he pays $150, and has it endorsed. Then two years after, he pays $75, and has it endorsed. At the end of six years he is ready to settle the note, and the question is, how much interest he shall pay.

There are different modes established by the laws of different states on this subject.

How find time, when principal, rate, and interest are known ?

The first

The three following are the most common. is the one which was formerly most commonly used.

FIRST METHOD.

Find the amount of the principal for the whole time.

Find the AMOUNT of each payment to the time of settle. ment.

Add the AMOUNTS of the payments, and subtract them from the AMOUNT of the principal.

EXAMPLE.

On April 1st, 1825, I gave a note to A. B. promising to pay him $300 for value rec'd. and interest on the same at 6 per cent. till settlement. Oct. 1, 1825, I paid $100. April 16, 1826, paid $50. Dec. 1, 1827,

paid $120. What do I owe on April 1st, 1828 ? $ cts, m. 300,00,0 principal dated April 1, 1825.

. 54,00,0 interest up to April 1st, 1828. 3. 0. 0.

ys, mo. da.

354,00,0 amount of principal.

100,00,0 1st payment, Oct. 1, 1825. 15,00,0 interest up to April 1st, 1828.

2. 6. 0.

115,00,0 amount of 1st payment.

50,00,0 2nd payment, April 16th, 1826. 5,87,5 interest up to April 1st, 1828.

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55,87,5 amount of second payment.

120,00,0 3rd payment, Dec. 1st, 1827.

2,40,0 interest up to April 1st, 1828.

0. 4. 0.

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115,00,0 amount of 1st payment.

293,27,5 total amount of payments.

354,00,0 amount of principal.
293,27,5 total amount of payments subtracted.

A. 60,72,5 remains due April 1st, 1828.

RULE IN MASSACHUSETTS.

Find the Amount of the Principal to the time when one payment, or several payments together, exceed the interest due. From this subtract the payments, and the remainder will be a new Principal. Proceed thus till the time of set. tlement.

EXAMPLES.

For value received, I promise to pay James Lawrence $116,666 with interest.

May 1st, 1822. $116,666.

John SMITH. On this note were the following endorsements. Dec. 25, 1822, received $16,666. July 10, 1823,

1,666. Sept. 1, 1824,

$ 5,000, June 14, 1825,

$33,333. April 15, 1826, $62,000. What was due August 3, 1827?

Ans. $23,775. The first principal on interest from May 1, 1822,

$116,666 Interest to Dec. 25, 1822, time of the first payment (7 months 24 days),

4,549

Amount, $121, 215 Payment, Dec. 25, exceeding interest then due, 16,666 Remainder for a new principal,

104,549

Interest from Dec. 25, 1822, to June 14, 1825 (29 months, 19 days),

15,490

Amount, $120,039 Payment, July 10, 1823, less than interest then due,

$ 1,666 Payment, Sept. 1, 1824, less than interest then due,

5,000 Payment June 14, 1825, exceed. ing interest then due,

33,333

$39,999

Remainder for a new principal (June 14, 1825),

Interest from June 14, 1825, to April 15, 1826 (10 months 1 day),

80,040

4,015

Amount, 84,055 Payment, April 15, 1825, exceeding inte. rest then due,

62,000

Remainder for a new principal (April 15, 1826),

Interest due Aug. 3, 1827, from April 15, 1826 (15 months 18 days),

$22,055

1,720

Balance due Aug. 3, 1827,

$23,775

The Rule now adopted in Connecticut, is founded on the principle that interest is to be paid by the year, so that if a man pays before a year is ended, he receives interest on all he pays, from the time he pays it, to the end of the year when the interest is due.

RULE IN CONNECTICUT.

If the payment be made at the end of a year or more, add the interest due on the whole sum, at this time, to the princi. pal, and subtract the payment.

Whenever other payments are made, proceed in the same

manner, calculating interest on the principal from the time of the last payment.

If payment is made before a year has elapsed (from the date of the note, or from the last payment), find the amount of the principal for one year. Find also the amount of the payment from the time of payment to the end of the year when the interest would be due, and subtract the latter from the former. If, however, a year extends beyond the time of settlement, find the amount up to that time, instead of for a year.

If any remainder after subtraction, be greater than the preceding principal, then the preceding principal is to be con. tinued as the principal

for the succeeding time instead of the remainder, and the difference to be regarded as so much unpaid interest.

Let interest on the following note be calculated by the three different rules.

A note for 20,000 is given July 1st, 1825. 1st payment, January 1st, 1826,

$1400 2d. do. January 1st, 1827,

2000 3d. do. September 1st, 1827,

5000 Settlement January 1st, 1829. What is due on the note ?

Answers.
By the common rule,

$14,908,00
By the Massachusetts rule,

15,212,96 By the Connecticut rule,

15,209,47 Let the following be calculate 1 by the Connecticut rule. $1000,00

Hartford, Jan. 4, 1826. On demand I promise to pay James Lowell, or order, one thousand dollars with interest; value received.

HIRAM SIMPSON.

On this note were the following endorsements.
Feb. 19, 1827, received

$200.00
June, 29, 1828,

500.00 Nov. 14, 1828,

260.00 Dec. 29, 1831,

25.00

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