Examples to Prop. 1.

(1.) An estate brings in 25l. yearly rent; required the present worth thereof, allowing the purchaser 4 per cent. compound interest for his money.

First, 104-104, the ratio less 1.

Then 2504 £625, the present worth required.

(2.) Suppose a freehold estate of 250l. yearly rent is to be sold; what is it worth, allowing the buyer 6 per cent. compound interest for his money?

(3.) What is the present worth of a freehold estate of 2501. per annum, the rent payable half yearly *, allowing the purchaser 4 per cent. for his money ?

(4.) What is the present worth of a perpetual annuity of 20007. payable quarterly, (viz. 500l. per quarter), allowing the buyer 4 per cent. compound interest for his money?

Examples to Prop. 2.

(5.) I propose to lay out 6251. in the purchase of a perpetual annuity, and to make 4 per cent. compound interest for my money; what ought the annuity to be?

104-104, the ratio less 1.

Then, 01×625=£25, the annuity or annual rent required.

(6.) A freehold estate was bought for 4166/. 13s. 4d. ; what ought the yearly rent to be, allowing the buyer 6 per cent, compound interest for ready money?

(7.) A person is desirous of laying out 17607. in the purchase of a freehold estate, so as to get 4 per cent. compound interest for his money; what must be the annual income of such an estate?

*It may not be improper to observe in this place, that, if the ratio be taken according to Table I. p. 242, it will make no difference whether the rents are payable yearly, half yearly, or quarterly, but, if it be taken according to Table II. page 242, the difference, in this example, will be 61l. 17s. 14d.: this shews, that the second method or table is more accurate than the first; for it is certainly more advan rageous to receive the rents half-yearly than yearly.

9

Examples to Prop. 3. :

(8.) Suppose 6254. to be paid for a freehold estate which yields 251. per annum, what rate of interest has the purchaser for his money?

625)25.00(04

1.

1.04 the ratio; hence the rate per cont. is 41. (9.) Suppose a freehold estate of 2501. per annum, costs 41667, 138. 4d., what rate of interest per cent, is allowed to the purchaser?

(10.) A freehold estate of 60%. a year rent was sold for 12007., what was the rate per cent. (compound interest) allowed the purchaser for the ready money which he paid for the estate?

THE BUYING AND SELLING FREEHOLD ESTATES TO BE ENTERED ON IMMEDIATELY, ACCORDING TO A NUMBER OF YEARS' RENT, OR INCOME, FOR THE PURCHASE-MONEY.

Proposition 1. The purchase-money, or present worth, of a freehold estate being given, to find at what rent it must be let to clear itself in a given time,

Rule. Divide the present worth by the proposed time, and the quotient will be the annual rent.

Prop. 2. Given the purchase, or present worth, of a freehold estate, and the annual rent it lets for, to find in what time it will clear itself, or bring in the purchase

money.

Rule. Divide the present worth by the annual rent, and the quotient will be the time required.

Prop. 3. Given the annual rent of a freehold estate, and the time in which it will clear itself, to find the purchase, or present worth, of such an estate.

Rule. Multiply the rent by the time.

Prop. 4. Given the time in which a freehold estate brings in the purchase money, or clears itself, to find what rate per cent. the purchaser has for his money.

Rule. Divide the time more 1 by the time, and the quotient will be the ratio, whence the rate may be found.

Prop. 5. When a person proposes to lay out any sum of money in a freehold estate, so that he may make a certain rate per cent. of the money laid out, to find in what time the estate will clear itself.

Rule Divide an unit by the ratio less 1, and the quo tient will be the time.

Examples to Proposition 1.

(1.) A freehold estate was purchased for 6251. At what rent must it be let that it may bring in the purchasemoney in 15 years?

625-15-413-411. 13s. 4d.

(2.) A freehold estate was purchased for 12007. At what rent must it be let to clear itself in 20 years?

Examples to Prop. 2.

(3.) I purchased a freehold estate for 45007. which I let at 250l. per annum ; in what time will it clear itself?

4500-250-18 years, answer.

(4.) I purchased a freehold estate for 6257., which brings me in 251. per annum; in what time will it clear itself?

Examples to Prop. 3.

(5.) If a freehold estate, which lets for 407. per ann. will clear itself in 20 years, what is its present worth?

40×20=£800, answer.

(6.) If a freehold estate, which lets for 25l. per ann. will clear itself in 25 years, what was it bought for?

Examples to Prop. 4.

(7.) If a freehold estate be sold for 20 years purchase, what rate per cent. compound interest is the purchaser allowed for his money?

20+1 21

20 20

105, the ratio. Hence the rate is 5 per cent.

(8.) If a freehold estate be sold for 223 years purchase, what rate per cent. is the buyer allowed for his money?

Examples to Prop. 5.

(9.) Suppose I want to lay out 12007. in a freehold estate, and to have 5 per cent. allowed me for my money; in what time will the estate bring in the purchase-money, or clear itself?

1-05-20 years, answer.

(10.) I wish to lay out 6257. in a freehold estate, and to have 4 per cent. allowed me for my money; in what time will the estate clear itself?

PURCHASING FREEHOLD ESTATES OR PERPETUAL

IN REVERSION.

ANNUITIES

Here the annuity or yearly rent; Tthe time before the annuity commences; p=the present worth; r the ratio, &c.

Proposition 1. The yearly rent of a freehold estate, and the rate per cent. being known, to find the present worth of the reversion of such an estate.

Rule. Find the present worth for the reversion (by Prop. 1, page 259.)

Then, by (Prop. 2, page 243) find what principal will amount to the full value of the estate for the time before it commences, and it will be the present worth required,

Theos I.

n

r-1xr

T=

when n, r, and T, are given.

=log. p.

Logarithmically. Log. n-log.rxT+log. r

Prop. 2. The sum given for the reversion of a freehold estate being known, to find the yearly income, allowing the purchaser so much per cent. for his money.

Rule. Find the amount of the purchase-money, to the time when the reversion begins, (by Prop. 1, page 243.) Then find the yearly income which that amount will purchase, (by Prop. 2, page 259,) and it will be the

answer.

Theo, H. 1xrTxp=n.

Logarithmically. Leg. r1+log. +XT+log. p.log. n.

Examples to Proposition 1.

(1.) The reversion of a freehold estate of 500l. per annum, to commence 5 years hence, is to be sold; what is it worth in ready money, allowing the purchaser 4 per cent. for his money?

500÷·04—125001. value of the estate, if entered on immediately. 1·04×1·04×1·04×1·04 × 1·04-12166529024, amount of 11, for

3 years.

1-2166529024 : 11.:: 12500: 10274.088834=£10274 1.9-281, present worth of the reversion..

Or thus by Theorem I.

Here n=500, r1.04, and T-5.

T

104×1.04x101×104 × 1'04—1·2166529024➡r1 and

1.2166529024 ×·04·048666116096=r1×T.

Hence 500-048666116096-10274-088834-£10274 1 91.281, as before.

(2.) If a freehold estate of 607. 10s. per annum, to commence 10 years hence, is to be sold; what is it worth, allowing the purchaser 5 per cent. for present payment?

(3.) A freehold estate of 2907. per annum, to commence 4 years hence, is to be sold; what is it worth, allowing the purchaser 4 per cent.?

Examples to Prop. 2.

(4.) A freehold estate, to commence 5 years hence, is sold for 102747. 1s. 9d281, allowing the purchaser 4 per cent. for his money; what is the yearly rent?

First,

10274 1 91281=10274-088834.

1.04X1.04x1·04 × 1·04 x 1.04-1.2166529024.

1-2166529024 × 10274 088834—12500 (nearly) the amount of the purchase-money to the time the reversion begins. Then, 12500×04 £500, the yearly rent.

By Theo. II.

0×1045×10274 0888841xrTxp=04× 1216652904×10274-088834 £500, (nearly) the annuity required. (5.) If a freehold estate, to commence 10 years hence, is sold for 7427. 16s. 8‡d 8, allowing the purchaser 5 per cent.; what is the yearly rent?