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To find the present Worth of a Freehold Estate, or an Annuity to continue for ever, at Compound Interest.

RULE.*

As the rate per cent. is to 100l. so is the yearly rent to the value required.

EXAMPLES.

*The reason of this rule is obvious: for since a year's interest of the price, which is given for it, is the annuity, there can neither more nor less be made of that price than of the annuity, whether it be employed at simple or compound interest.

The same thing may be shewn thus: the present worth of an

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as has been shewn before; but the sum of this series, by the rules

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The following theorems shew all the varieties of this rule.

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The price of a freehold estate, or annuity to continue for ever,

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at simple interest, would be expressed by ++

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+

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1+ 3r

1+4r

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&c. ad infinitum ; but the sum of this se

ries is infinite, or greater than any assignable number, which sufficiently shews the absurdity of using simple interest in these

cases.

EXAMPLES.

1. An estate brings in yearly 791. 4s. what would it sell for, allowing the purchaser 4 per cent. compound interest for his money?

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2. What is the price of a perpetual annuity of 401. discounting at 5 per cent. compound interest ? Ans. 8ool.

What is a freehold estate of 751. a year worth, allowing the buyer 6 per cent. compound interest for his money? Ans. 1250l.

To find the present Worth of an Annuity, or Freehold Estate, in Reversion, at Compound Interest.

RULE.* *

1. Find the present worth of the annuity, as if it were to be entered on immediately.

2. Find

* This rule is sufficiently evident without a demonstration. Those, who wish to be acquainted with the manner of computing the values of annuities upon lives, may consult the writings of Mr. DEMOIVRE, Mr. SIMPSON, and Dr. PRICE, all of whom have handled this subject in a very skilful and masterly manner.

Dr.

2. Find the present worth of the last present worth, discounting for the time between the purchase and commencement of the annuity, and it will be the answer required.

EXAMPLES.

1. The reversion of a freehold estate of 791. 4s. per annum, to commerce 7 years hence, is to be sold; what is it worth in ready money, allowing the purchaser 41⁄2 per cent. for his money

?

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and 1045 = 1360862)1760*000(1293°297 = 12931. 5sid. present worth of 1760l. for 7 years, or the whole present worth required.

2. Which is most advantageous, a term of 15 years in an estate of 100l. per annum, or the reversion of such an estate forever, after the expiration of the said 15 years, computing

Dr. PRICE'S Treatise upon Annuities and Reversionary Payments is an excellent performance, and will be found a very val uable acquisition to those, whose inclinations lead them to studies of this nature.

DE

computing at the rate of 5 per cent. per annum, compound interest?

Ans. The first term of 15 years is better than the reversion for ever afterward, by 751. 18s. 7d.

3. Suppose I would add 5 years to a running lease of 15 years to come, the improved rent being 1861. 7s. 6d. per annum; what ought I to pay down for this favour, discounting at 4 per cent. per annum, compound interest? Ans. 460l. 14s. 13d.

POSITION.

POSITION is a method of performing such questions, as cannot be resolved by the common direct rules, and is of two kinds, called single and double.

SINGLE POSITION.

Single Position teaches to resolve those questions, whose results are proportional to their suppositions.

RULE.*

1. Take any number and perform the same operations with it, as are described to be performed in the question.

2. Then say, as the result of the operation is to the position, so is the result in the question to the number required.

EXAMPLES.

* Such questions properly belong to this rule, as require the multiplication or division of the number sought by any proposed number; or when it is to be increased or diminished by itself, or any parts of itself, a certain proposed number of times. For in

EXAMPLES.

1. A's age is double that of B, and B's is triple that of ̧ C, and the sum of all their ages is 140: what is each person's age?

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2. A certain sum of money is to be divided between 4 persons, in such a manner, that the first shall have of it ; the second; the third; and the fourth the remainder, which is 281.: what is the sum ? Ans. 1121

3. A person, after spending 6ol. left: what had he at first ?

and of his money, had Ans. 1441.

4. What number is that, which being increased by

and of itself, the sum shall be 125 ?

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Ans. 60.

5. A

this case the reason of the rule is obvious; it being then evident, that the results are proportional to the suppositions.

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NOTE.

I may be made a constant supposition in all questions;

and in most cases it is better than any other number.

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