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COMPOUND INTEREST.

374. COMPOUND INTEREST is interest on the original principal with its interest added when remaining unpaid after becoming due.

When the interest is added to the principal at the end of every year, and a new principal is thus formed yearly, it is said to compound annually; when the interest is added to the principal so as to form a new principal half-yearly, it is said to compound semiannually.

375. Compound interest is based upon the principle, that, if the borrower does not pay the interest as it becomes due at stated times, it is no more than just for him to pay interest for the use of it, so long as he shall have it in his possession.

NOTE. Compound interest is not favored by the laws, though it is not usurious. A contract or promise to pay money with compound interest cannot generally be enforced, being only valid for the principal and legal interest.

376. To find the compound interest of any sum of money at any rate per cent. for any time.

Ex. 1. What is the compound interest of $ 300 for 3 years?

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Comp. int. for 3 years, $5 7.30 48, Ans.

We first multiply the given principal by the number denoting the interest of $1 for one year, and add the interest thus found to the principal for the amount; on which as a new principal we find the interest for the second year, and proceed as before; and so also with the third year. From

the amount of the last year we subtract the first principal, and obtain the compound interest for 3 years.

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Compound interest for 4 years, $57.304 Ans.

[at 6 per cent.

In the second operation the work is somewhat abridged, by finding the interest for each year at 6 per cent. by taking of the principal for the interest at 5 per cent., and of that for interest at 1 per

cent.

RULE. Find the interest of the given sum to the time the interest becomes due, and add it to the principal. Then, find the interest on this amount as a new principal, and add the interest to it, as before. Proceed in the same manner for each successive period when the interest becomes due until the time of settlement.

Subtract the principal from the last amount, and the remainder will be the compound interest.

NOTE. When partial payments have been made on notes at compound interest, it is customary to find the amount of the given principal, and from it to subtract the sum of the several amounts of the indorsements.

EXAMPLES.

2. What is the amount of $500 for 3 years at compound interest? Ans. $595.508. 3. What is the compound interest of $970 for 2 years 9 months and 24 days? Ans. $173.295. 4. What is the compound interest of $300 for 4 years 6 months, at 7 per cent.? Ans. $107.001. 5. What is the compound interest of $316 for 3 years 4 months and 18 days? Ans. $69.017.

377. The computation of compound interest is rendered more expeditious by means of the following

TABLE,

OWING THE AMOUNT OF ONE DOLLAR AT COMPOUND INTEREST FOR ANY NUMBER OF YEARS NOT EXCEEDING FIFTY.

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NOTE. — If each of the numbers in the table be diminished by 1, the remainder will denote the interest of $1, instead of its amount.

12.250 455 18.344 355

Ex. 1. What is the compound interest of $ 360 for 5 years

6 months and 24 days?

Amount of $1 for 5 years,
Principal,

OPERATION.

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We find the amount of $1 for 5 years in the table, and, multiplying it and the number denoting the given principal together, obtain the amount of the $360 for 5 years. On this amount as a new principal we find the amount for the remaining 6 months and 24 days, by multiplying by the number denoting the amount of $1 for the same time. From the last amount subtracting the original principal, we have left the compound interest required. Hence,

Multiply the amount of $1 for the given time and rate, as found in the table, by the number denoting the given principal. The product will be the required amount, from which subtract the given principal, and the remainder will be the COMPOUND INTEREST.

NOTE. When the given time includes not only the regular periods at which interest becomes due, but also a partial period, as a succession of periods of a year each, followed by one containing months or days, or both, after finding the amount for the regular periods, multiply that amount by the amount of $1 for the remaining time or partial period, and the product will be the required amount for the given time. In like manner, when the number of successive periods exceeds the limits of the table, make the computations for a convenient length of time by means of the table, and on the amount thus found make another computation by means of the table, and so on.

In making computation for a succession of periods shorter or longer than one year each, use the numbers in the table the same as if the periods were those of one year each.

EXAMPLES.

2. What is the compound interest of $1200 for 11 years at Ans. $1325.822.

per

cent.?

3. What is the compound interest of $300 for 10 years 7 months and 15 days? Ans. $257.401. 4. What is the compound interest of $5 for 50 years at 7 per cent.? Ans. $142.285.

5. What is the amount of $480 for 40 years, at compound interest? Ans. $4937.144. 6. What is the compound interest of $ 40 for 4 years, at 7 per cent.? Ans. $12.431. 7. What is the compound interest of $100 for 100 years? Ans. $33830.20.

8. What is the difference between the simple and the compound interest of $1000 for 33 years and 4 months?

9. To what sum will $50, deposited in a savings bank, amount, at compound interest for 21 years, at 3 per cent., payable semiannually? Ans. $173.034.

(10.) $100.

Boston, September 25, 1853.

For value received, I promise to pay J. D. Forster, or order, on demand, one hundred dollars, with interest, after six months. ALLEN T. DAWES.

On this note are the following indorsements: dollars; September 25, 1854, received fifty dollars.

June 11, 1854, received fifty

What was due, reckoning at compound interest, August 25, 1855 ? Ans. $2.247.

(11.) $1000.

St. Paul, January 1, 1850. For value received, I promise to pay Stephen Howe, or bearer, on demand, one thousand dollars, with interest at 7 per cent. WILSON GOodhue.

Indorsements:- -June 10, 1850, seventy dollars; September 25, 1851, eighty dollars; July 4, 1852, one hundred dollars; November 11, 1853, thirty dollars; June 5, 1854, fifty dollars.

At 7 per cent. compound interest, what remains due April 1, 1855 ? Ans. $1022.34.

378. To find the PRINCIPAL, the compound interest, the time, and the rate being given.

Ex. 1. What principal at 6 per cent. compound interest will produce $2370 in 10 years? Ans. $3000.

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