Imágenes de páginas
PDF
EPUB

to the given rate per cent. for quarterly or half yearly payments, will be the true amount.

TABLE SECOND.

Rate per cent.

Half yearly

payments.

Quarterly pay

ments.

The construction of this table is from an Algebraic Theorem given by the learned Mons. De Moivre, in his Treatise

of Annuities on Lives, 3 1,007445 1,011181

which in words is thus: 3 1,008675 1,013031 For half yearly payments 4 1,009902 1,014877 take a unit from the ra4} 1,011126 1,016720

tio, and from the square 5 1,012348 1,018559 54 1,013567 1,020395

root of the ratio, half the 6 1,014781 1,022257 quotient of the first re7 1,017204 1,025880 mainder, divided by the

latter will be the tabular number; for quarterly payments, use the fourth toot, as above, and take one-fourth of the quotient.

1. What will an annuity of $200 amount to in 5 years, to be paid in half yearly payments, at 6 per cent. per annum?

Ans. $1144 8c. 2m. to Agreeably to table first, the tabular number is 5.63709 x 200 = $1127 41c. 8m. x 1.014781, (tabular number answering to 6 per cent. in table second, for half yearly payments) $1144.08.2m. + answer.

2. What will an annuity of $500 amount to in 5 years, at 6 per cent.?

Ans. $2818.54.6 +. 3. What will an annuity of $1000, payable yearly, amount to in 10 years?

Ans. $13180.79.4 +. 4. What will annuity of $30, payable yearly, amount to in 3 years?

Ans. $95.50.8 +.

ANNUITIES.

Table Third, shewing the present worth of an Annuity of $1, from One year to Thirty-seven.

Yrs. 5

per cent. 6

per cent. | Yrs. 5 per cent. | 6

per cent. Yrs, 5

per cent. 6

per

cent.

14 9,898641

0,952381 0,943396
2 1,859410 1,833393

2,723248 2,673012
4 3,545950 3,465106
5 4,329477 4,212364
6 5,075692 4,917324
7 5,786373 5,582381
8 6,463213 6,209794
9 7,107822 6,801692
10 7,721735 7,360087
11 8,306414 7,886875
12 8,863252 8,388844
13 9,393573 8,852683

14 9,898641 9,294984
15 10,379658 9,712249 | 27 14,643034 13,210534
16 10,83770 10,105895 28 14,898127 13,406164
17 11,274066 10,477260 29 15,141074 13,590721
18 | 11,689587 10,827603 30 (15,372451 13,764831
19 12,085321 | 11,158116 31 15,592810 13,929086
20 12,462216 11,469921 32 15,802677 14,084043
21 12,821153 11,764077 33 16,002549 . 14,230230
22 13,163003 12,041582 34 16,192904 14,368141
23 13,488574 | 12,303379 35 16,374194 14,498246
24 13,798642 12,550358 36 16,546852 14,620987
25 14,093945 12,783356 37 (16,711287 14,736780
26 ( 14,375185 (13,003166

EXPLANATION OF THE TABLE. What is the present worth of $1, to continue for 4 years at 6 per cent. per annum? Ans. 3.465106, agreeing with the tabular number opposite to 4 years at 6 per cent. per annum.

First, find the present worth of $1, by discount for 1 year at 6 per ct. per annum, which is $0.943396 2d year the present worth is

0.889996 3d

is

0.839619 is

0.792094

4th 66

$3.465105 Tabular number for 4 years at 6 per. cent. as in table 3d.

1. What is the present worth of $50 per annum for 6 years at 6 per cent. per annum? Ans. $245.86c. 6m.

CASE III.

Annuities in Reversion. The annuity, time, and rate given, to find the present worth as in case 2. Multiply the number, under the rate and opposite th etime in table 3d, by the annuity, the product will be the present worth for yearly payments. If the payments are to be made half-yearly, or quarterly, the present worth so found for yearly payments, must be multiplied by the proper number in table 2d.

Q. What is meant by annuities in reversion?

A. Sums of money, which are paid yearly for a limited period, but which do not commence till after the expiration of a given period, are called annuities in reversion. Given the time of reversion, time of continuance and rate

per cent. to find the present worth of the reversion. RULE.—Take two numbers under the given rate in table 3, corresponding to the different periods of time, viz; time of reversion and time of continuance, and take the difference between the tabular numbers, answering to the times as above mentioned, and multiply that difference by the

[ocr errors][ocr errors]

annuity, for the present worth annually, if the payments be half yearly or quarterly, we must use table 2 as above stated.

1. The reversion of a freehold is $60 per annum for 4 years, to commence 2 years hence, what is the present worth, allowing 6 per cent. for prompt payment.

Illustration.-Time of continuance 6 years. Tabular number for 6 years at 6 per cent. found in table 3, is

4.917324 Time of reversion; 2 years tabular No. 1.833393

3.083931 3.083931 x 60 $185.03c.5m. x Answer.

2. What is the present worth of a reversion of a lease of $100 per annum, to continue 10 years; but is not to commence till the end of 2

years
at 6
per

cent.

Ans. $655.041. 3. What is the present worth of a reversion of a lease for $120 per annum to continue 9 years, but not to commence till the end of 4 years at 5 per cent to the purchaser?

Ans. $701.71c. 4m.

PERPETUITIES. Annuities which continue for ever, are called perpetuities.

CASE IV.

Given the Annuity and rate per cent. to find the present

worth, RULE.—Divide the annuity by the ratio less 1, for the present worth.

Note.--Table 2d must be resorted to, as in temporary annuities, when the payments are half-yearly or quarterly.

1. What is the present worth of an annuity of $150 to continue for ever, allowing 5 per cent. to the purchaser? Operation.-1.05–1 = .05)150.00

$3000 Ans.

2. What is an estate of $260 per annum, to continne for

ever, worth in present money, allowing 6 per cent. to the purchaser?

Ans. $4333.33.3 +. 3. A property in fee simple rents for $120 per annum, what is the present worth, allowing 5 per cent. to the purchaser?

Ans. $2400.

DISCOUNT BY COMPOUND INTEREST. The ratio in compound interest is the amount of $1 for one year, which is found thus: as 100 : 106 : :1 = $1.06 is the amount of $1 for one year.

Example 1.—What is the present worth of 600 for 3 years; hence at 6 per cent. compound interest 1.063 = 1.191016)600( = $503.77 + Ans.

2. What is the amount of $503.77, in 3 years at 6 per cent.?

Ans. $600. 3. What is the present worth of $520, due 5 years hence, at 6 per cent. compound interest. Here 520 1,3312256)520(=390.62 answer.

1.065

ALLIGATION, From the Latin (ad. to, and ligo to bind,) it being necessary in sundry cases to link or bind the quantities.

We shall not omit the rule of Alligation, the object of which is to find the value of several things of the same kind of different values. The following examples will sufficiently demonstrate it.

CASE I.

When the quantities and rates of the simples are given to find the rate of a mixture compounded of these simples.

Rule.--Find the value of each quantity, according to their respective costs, then divide the sum of the pro

« AnteriorContinuar »