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yrs.

1

2 2,050000

A TABLE.

Showing the amount of $1 or £1 annuity at 5 and 6 per cent for any number of years, not exceeding 34.

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6 per cent.
5 per cent.
1,000000 18 28,132385
2,060000 19 30,539004

6 per cent.

30,905653

33,759992

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79,058186

13 17,712983 18,882138 30 66,438847 14 19,598632 21,015066 31 70,760790 15 21,578564 23,275969 32 75,298829 16 23,657492 25,672528 33 80,063771 17 25,840366 28,212380 34 85,066959 104,183754|

84,801677 90,889778 97,343165

To find the amount of an annuity by this Table. RULE.-Opposite the given year and under the rate per cent you will find the amount of $1 for the given time. Multiply this amount by the given annuity.

2. If a salary of $90 per annum, to be paid yearly, remain in arrears 12 years, what will be its amount at 5 per cent compound interest?

Tabular amount 15,917126

given annuity

X 90

Ans. $1432,541340-$1432,54c. 1,34m. 3. What is the amount of an annuity of $100 remaining unpaid, or in arrears 20 years, at 6 per cent compound interest? Ans. $3678,55c.92m. 4. If an annual pension of $130 remain in arrears 7 years, what is the amount due, at 6 per cent compound inAns. $1091,19c.88m. 5. What would $50 annuity amount to at 6 per cent compound interest, for 33 years? Ans. $4867,15c.8+m.

terest?

CASE II.

To find the present worth of annuities.

The present worth here spoken of, is such a sum as if put at compound interest for the given rate and time will be equal to the amount of the given annuity.

RULE.

Raise the ratio to a power equal to the given number of years. Then divide the annuity by that power, and subtract the quotient from the annuity, and divide the remainder by the ratio, less 1.

EXAMPLES.

1. What sum of ready money will purchase a yearly annuity of $60, to continue 4 years, at 6 per cent?

Ratio 1,06 × 1,06 × 1,06 × 1,06=

1,26247696)60,00000000000(47,5256+

then from the annuity 60,0000

subtract this quotient 47,5256

ratio 1,06-1=;06)12,4744

Ans. $207,906+$207,90c. 6m.+

TABLE II.

Showing the present worth of an annuity of $1 or £1, at 5 and 6 per cent for any number of years from 1 to 32.

yrs

12345

4

5 per cent.

0,952381

1,859410 2,723248

6 per cent.

0,943396

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17 11,274066 | 10,477260 1,833393 18 11,689587 10,827603 2,673012 19 12,085321|11,158116 3,545950 3,46510620 12,46221011,469921 4,329477 4,212364|21| 12,821153| 11,764077 6 5,075692 4,91732422 13,163003 12,041582 7 5,786278 5,58238123 13,48857412,303380 8 6,463213 6,209794 24 13,798642 12,550357 97,107822 6,801692 25 14,093944 12,783356 10 7,721735 7,360087 26 14,37518513,003166 11 8,306414 7,88687527 14,643034 13,210534 12 8,863252 8,383844 28 14,898127 | 13,406164 13 9,393573 8,852683 29 15,141073 13,590721 14 9,898641 9,294984 30 15,372451 9,712249 31 15,592810 13,929080

15 10,379658

13,764831

16 10,837769 10,105895 32 15,802681 14,084042

RULE.

Multiply the present worth, found in Table II. opposite the given year, and under the rate per cent, by the given annuity.

2. What is the present worth of an annuity of $200, to continue 10 years, at 6 per cent?

by Table II. present worth of $1 for 10yrs. 7,360087

Ans. $1472,1c.74m.

X 200 $1472,017400

3. How much must be paid in ready money, to purchase an annuity of $156 to continue 8 years at 5 per cent ? Ans. 1008,26c.1m.+ 4. What is the present worth of an annual pension of $96 a year, to continue 5 years at 6 per cent compound interest ? Ans. $404,38c.6m.+. 5. What ready money will purchase an annuity of $112 to continue 30 years, at 5 per cent compound interest? Ans. $1721,71,45+.

CASE III.

To find the present worth of annuities, leases, &c. taken in reversion at Compound Interest.

Observation.- Annuities in reversion, are those which do not commence till some particular event has happened, or until the expiration of a certain time.

RULE.

1. Divide the annuity by the power of the ratio equal to the time of its continuance, and subtract this quotient from the annuity, and divide the remainder by the ratio less 1, and the quotient will be the present worth to commence immediately.

2. Divide the quotient by the power of the ratio equal to the time of reversion, (or the time to come before the annuity commences,) and the quotient will be the present worth of the annuity in reversion.

1. What is the present worth of $200, payable yearly for 4 years but not to commence, (that is being in reversion,) till the end of 2 years, at 6 per cent ?

4th power of 1,06 1 26247696)200,00000000(158,418732

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It will be much easier to find the present worth of annuities in reversion, by 2d Table. Thus, find the present worth of $1, or £1, annuity for the sum of the time of reversion and the time of continuance added together; and from this present worth, subtract the present worth of $1 or £1 for the time of reversion, and multiply the remainder by the given annuity.

2. What is the present worth of $50 yearly annuity to continue 8 years, and to be in reversion 3 years at 5 per cent ? Time of reversion, or the time before the annui

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The present worth of $1 for 11 yrs. by 2d Table, 8,306414

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3 yrs. reversion

Remainder

2,723248

5,583166

X 50

Ans. $279,158300

3. What is the present worth of the reversion of a lease of $125 to continue 20 years, but not to commence till the end of 9 years, allowing 6 per cent?

Ans. $848,62c.8+m. 4. What sum of ready money will purchase the reversion of an annuity of $60 to continue 15 years, but not to commence till the end of 10 years, at 5 per cent ? Ans. $382,33c.2+m.

CASE IV.

To find the present worth of freehold estates, or annuities to continue forever.

RULE.

As the rate per cent is to 100, so is the yearly rent or annuity to the value required. Or, divide the yearly rent

or annuity by the rate per cent, and the quotient will be the annuity.

EXAMPLES.

1. What is the worth of a freehold estate of which the yearly rent is $50, allowing to the purchaser 5 per cent? 5 100 50 $1000 Ans.

or,,05)50,00(1000 Answer as before.

2. What is the worth of $125 annuity to continue for ever, allowing 6 per cent to the purchaser ?

Ans. $2083,333. 3. What is the value of an estate which brings in yearly, $96, allowing 6 per cent to the purchaser? Ans. $1600.

CASE V.

To find the present worth of perpetual annuities or freehold estates in reversion at Compound Interest.

RULE.

Find the present worth of the estate by the Rule, Case 4th, which will give the value if entered on immediately. Then divide that value by the power of the ratio denoted by the time of reversion, and the quotient will be the present worth of the annuity in reversion.

EXAMPLES.

1. Suppose a freehold estate of $50 per annum to commence 2 years hence, be put on sale, what is its value, allowing the purchaser 5 per cent ?

5100 50 $1000 present worth if entered on immediately.

$ cts.m.

the ratio1,05 2d power 1,1025)1000,0000(907,02,9+ Ans. By Table 2, find the present worth of the annuity or rent for the time of reversion, which subtract from the value of the annuity found by Case IV.

By Tab. 2d, the present worth of $1 for 2yrs.

Present worth for the time of reversion,

1,859410 X 50

92,970500

Value of immediate possession,

1000,0000

92,9705

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