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From the amount=1235,975
950,75x5=4753,75)285,2250(,06=6 per cent. Ang.
2. At what rate per cent. will £543 amount to £705 18s. in 5 years ?
Ans. 6 per cent. 3. At what rate per cent. will $2124,25 amount to $3482,44284375 in 74 years? Ans. 8) per cent.
Case. 4.—The amount, principal, and rate per cent.
given, to find the time. · RULE.-Subtract the principal from the amount ; divide the remainder by the product of the ratio and principal; and the quotient will be the time.
From the amount $270,7451 .
TO CALCULATE INTEREST FOR DAYS.
A TABLE OF RATIOS FOR DAYS.
615,00017808219 515,00015068493 i 7 =,00019178082
Rule.-Multiply the principal by the given number of days, and that product by the ratio for a year ; divide the last product by 365, (the number of days in a year,) and it will give the interest required. Or, multiply the ratio for a day in the foregoing table by the principal, and that product by the given number of days; and the last product will be the interest required.
EXAMPLES. : 1. What is the interest of £360,10s. for 146 days, at 6 per cent. ?
360,5X146 ,06 £. £. 8. d. gr.
- =8,052=8 13 0 1,92 Ans.
365 Or ,00016438356X360,5x146=£8,6519999+ Ans.
2. What is the interest of $780,40cts. for 100 days, at 6 per cent. per annum ? Ans. $12,82cts. Am. +
3. What is the interest of $481,75cts. for 25 days at 7 per cent. per annum ?
Ans. $2,30cts. 9m. + NOTE.—The interest of any sum for 6 days, at 6 per cent., is just as many mills and decimals of a mill, as the principal contains dollars and decimals of a dollar. Therefore set down the principal, multiply it by the days, and divide the product by 6; the quotient will be the interest in mills and decimals of a mill. This is calling only 30 days a month.. What is the interest of 8231,84 for 100 days? 231,84 x 100
Or 83,86 4; which is 5cts. Im. too much; but when the time is less than 30 days, it gives the answer very exact, for ordinary sums.
When interest is to be calculated on cash accounts, &c. where partial payments are made, it is the common practice to multiply the several balances into the days they are at interest; then to multiply the sum of these products by the rate on the dollar, and divide the last product by 365,; and thus cast the whole interest due on the account, &c.
EXAMPLE. Lent John Joy, per bill on demand, dated 1st of June, 1821, $2000, of which I received back the 19th of August, $400; on the 15th of October, $600; on the 11th of December, $400; on the 17th of February, 1822, $200; and on the 1st of Juve, $400 ; how much interest is due on the bill, reckoning at 6 per cent. ?.
Balance, 1000 Dec. 11. Received in part,
Balance, 400 104
$ cts. m. 365)23316,00(63,879+ Ans.=63,87 9
COMPOUND INTEREST BY DECIMALS. A table shưwing the amount of £1 or $1 at 5 and 6 per
cent. per annum, compound interest, for 20 years. Yrs.15 per cent. 6 per ct. | Yrs. I 5 per cent. | 6 per cent:
1,05000 1,06000 11 1,71033 1,296 29 1,10250 1,12360 12
1,79585 2,01219 1,15762 1,19101 | 13 1,88564 2,13292 1,21550 1,26247 | 14 | 1,97993 2,26090 1,27628 | 1,33822 15 2,07892 2,39655 1,34009 | 1,41851
2,18287 2,51035 1,40710 | 1,50363
2,29201 2,69277 1,47745 | 1,59384 18 2,40661 2,85433
1,55132 1,62947 / 19 2,52695 3,02559 10 1,62889 1,79084 | 20 2,65329 3,20713
Rule.—Multiply the given principal continually by the amount of one pound, or one dollar, for one year, at the rate per cent. given, until the number of multiplications is equal to the given number of years, and the product will be the amount required.
Or, Take from the preceding Table, the amount of one pound, or one dollar, as the case may be, for the given number of years, and at the given rate per cent., and multiply it by the given principal, and it will give the amount as before.
EXAMPLES. 1. What will £400 amount to in 4 years, at 6 per cent. per annum, coinpound interest ?' 400 x1,06x1,06x1,06 X 1,06=£504,99 +or £504 198.
9d. 2,4qrs. + Ans. Or, by the Table. Tabular amount of £1=1,26247 Multiply by the principal
Whole amount £504,98800 2. What is the compound interest of $555 for 14 years, at 5 per cent. ?
Ans. $543,86cts. + Note.--Any sum of money, at 6 per cent. per annum, simple interest, will double in 16 years ; but at 6 per cent. per annum compound interest, it will double in 11 years and 325 days, or 11,889 years. ANNUITIES AT COMPOUND INTEREST.
Case 1.-To find the amount of an annuity, foc.
RULE --Raise the amount of $1, or £1, at the given rate per vent., for one year, to that power denoted by the given number of years; subtract unity or 1 froin this product; multiply the remainder by the given annuily; divide this last produci by the ratio made less by unity or l; and the quotient will be the amount sought.
EXAMPLES. - 1. If $250, yearly pensjon, be forborne 7 years, what will it amount to, at 6 per cent. per annum compound interest. 1,06 x 1,06X 1,06x1,06X1,06X1,06 x 1,06 1,x250
2. If a salary, or an annuity, of £100 per annum, runs on unpaid for 6 years, at 5 per cent. compound interest, what is the amount due at the end of that period ?
Ans. £680 3s. 9 d. ,63.. CASE 2.- To find the present worth of an Annuity, f'c.
Rule.—Raise the amount of $1, or £1, at the given rate per cent., for 1 year, to that power denoted by the given number of years; divide the given annuity by this product ; subtract its quotient from the given annuity; divide the remainder by the ratio made less by unity or 1; and the quotient will be the present worth sought.
EXAMPLES 1. What is the present worth of a salary of $300, to continue 5 years, at 5 per cent. compound interest ? 300
=235,0578499405. + 1,05X1,05x1,05X1,05 x1,05 300—235,0578499405
-=1293,84 3+Ans. 1,05–1, 2. What is the present worth of £30 per annum, to continue 7 years, at 6 per cent. compound interest ?
Ans. £167 9s. 5d. +
INVOLUTION. INVOLUTION is the continual multiplication of a number into itself; and the products thence arising, with the original number itself,are called the powers of that number.
Any number may itself be called a first power. If the first power be multiplied by itself, the product is called the second power, or square ; if the square be multiplied by the first power, the product is called the third power, or cube; if the cube be multiplied by the first power, the product is called the fourth power, or biquadrate, &c.
Thus 3 is the first power of 3. 3x3=9 is the second power of 3. 3x3x3=27 is the third power of 3.
3x3x3x3=81 is the fourth power of 3, &c. &c. And in this manner is formed the following table of powers.