CHAP. I.

THE first Table which offers it self for Renewing of Leases, is for the term of 21 Years, it shews the values in Years, Quarters, Months, and Decimal parts of a Month, as all the rest do, the first part of this Table is calculated at 11 l. 11 s. 8 d. ¼, 1/10, per cent. per An. Com­pound Interest, so that the Fine for Renew­ing 7 Years Lapsed, or the present worth of 7 Years in Reversion, not to begin till 14 are expired, is exactly 1 Years Value, which Fine, and consequently rate of In­terest, Bishops, Deans and Chapters Heads and Fellows of most Colleges in both Uni­versities, do observe in Letting and Re­newing of their Leases; but at other rates of Interest, the Fine for Renewing 7 Years Lapsed, the Table shews as followeth, viz.

The years in esse may be valued as a Lease of so many years, as in this Lease of 21 years, if 7 years are run out, then there are 14 in esse, whose value are as a Lease of 14 years, and may be found by the Table for Purchasing; or if you subtract the value of the years in Reversion from the value of the whole Lease, the remain­der is the value of the years in esse.

To find the value of some of the years in Reversion, as suppose 3 of the 7, I do thus, because 3 wants 4 of 7, I take the value of 4 years in Reversion, from the value of 7 in Reversion, the remainder is the value of the 3 years required.

Example.

Which remainder being given for a Fine, will make up the Lease to 17 years, that is 3 added to 14.

CHAP. II.

THE next Table is for the term of 20 years, the first part thereof is calcu­lated according to the rate of about 12 lb. 6 s. per cent. per An. so that 1 year's value is the worth of 7 years lapsed, or in Re­version; which Fine, and consequently rate of Interest, by some is observed in a Lease for 20 years; but at other rates of Interest: The Fine for Renewing 7 years lapsed in this Lease of 20 years, you will find by the Table as followeth, viz.

The years in esse may be valued as a Lease of so many years, or their value may be found, by subtracting the value of the years lapsed, from the value of the whole Lease, as was directed before in the Lease of 21 years.

The value of some of the years in Re­version may also be found in this Lease, as is directed before in the former Lease, however to make all plain, I shall give one Example: As suppose, I am to find the value of 4 of the 7 years in Reversion in this Lease; then according to the Rule given in the Lease of 21 years, I do thus, because 4 wants 3 of 7, I take the value of 3 years in Reversion, from the value of 7 in Reversion, the remainder is the value of the 4 years required.

Example.

this Remainder being given for a Fine will make up this Lease to 17 years, that is 4 added to 13.

CHAP. III.

THE third Table for Renewing of Leases, is for the term of 40 years, it is calculated according to five several rates of Interest, and in it's manner of using differs not from the other, nevertheless an Example will be convenient, which there­fore I shall give; as suppose there be 14 years lapsed or run out in a Lease for 40 years, What must I give to make up this Lease again, according to those several rates of Interest signified by the Table? that is, What must I give for 14 years in Re­version, after 26 in esse? or, What's the present Worth of 14 years, beginning 26 years hence? For answer I find by the Ta­ble that the Fine for Renewing 14 years lapsed

The years in esse, as was said before, are valued as a Lease of so many years, [Page 8]as in a Lease for 40 years, if 14 years are run out, then there are 26 in esse, whose Value are as a Lease of 26 years, and may be found by the Table for Purchasing, &c.

The Value of some of the years in Re­version, may be found in this Lease, by the same Rules that they were found by in the foregoing Leases; as if it were re­quired to find the Value of 6 of the 14 years in Reversion in this Lease of 40 years, then because 6 wants 8 of 14, I take the Value of 8 years in Reversion from the Value of 14 in Reversion, and the Remainder is the Value of the 6 years required, which will make the Lease up to 32 years.

CHAP. IV.

THis being the last Table for Renew­ing of Leases, is for the term of 10 yeares, the first part thereof is calculated according to the rate of about 17 l. 18 s. per cent. so that the Fine for Renewing 4 years lapsed is one years value, but at [Page 12]other rates of Interest, the Fine for Re­newing 4 years lapsed, is by the Table as followeth, viz. the Fine for Renewing 4 years lapsed

The years in esse are valued as before directed in the other Leases, as, if there be 4 years run out in this Lease of 10 years, then there are 6 years in esse, whose Value are as a Lease of 6 years, &c.

CHAP. V.

THE next Table is for the Reduction of the Values given in Years, Quar­ters, Months, and Decimal Parts of a Month, into Pounds, Shillings, and Pence, the use of it is very plain and easie, as by Examples will appear.

Example.

Suppose the Fine for Renewing any num­ber of years lapsed, in any Lease to be 6 y. [Page 13]2 q. 2 m. 4 d. p. and the yearly Rent 55 l. What is this Fine in Pounds, Shillings, and Pence? then by the Table I find

Which is the Value reduced into Pounds, Shillings, and Pence required.

Suppose again the Fine for Renewing any number of years lapsed in any Lease, to be 2 y. 3 q. 2 m. 9 d.p. and yearly Rent 156 l. then what is this Fine in Money? For answer I say, twice 156 is 312 l. which [Page 14]is the 2 years Value, then by the Table I find

Which is the Fine reduced into Money required, in like manner is any other Fine reduced, at any other yearly Rent from [Page 15]1 l. to 600 l. a year, or if it be more, it is but adding, after the same manner as is done in the Examples, as suppose the Rent to be 700 l. per An. then I must find the Values for 600 l. and for 100 l. and add them together, &c.

[Page 17]

CHAP. VI.

THE way of Purchasing by Lives was commonly to reckon one Life as a Lease of 7 years, two Lives as a Lease of 14 years, and three Lives as a Lease of 21 years: but this way seeming unequal, there is another way which is more agree­able to reason, and it is this, viz. for every Life to decrease one year, as if one Life be reckoned as a Lease for 10 years, then two will be as a Lease of 19, and three as a Lease of 27 years, &c. so that at 7 l. per cent. one Life is reckoned worth a little above 7 years purchase, two Lives 10 years, 1 quarter, and 1 month's purchase, &c. as the Table for Purchasing of Lives sheweth.

So if you reckon one Life as a Lease of 9 years, then 2 will be as a Lease of 17, three as a Lease of 24, &c. as is evi­dent by the Table; and one Life will be worth above 6 years and 2 quarters pur­chase, 2 Lives 9 years and 3 quarters pur­chase, [Page 19]3 Lives 11 years, 1 quarter, 2 months, and 6 Decimal Parts purchase, &c.

So if one single Life be reckoned as a Lease of 12 years, then two will be as a Lease of 23, three as a Lease of 33 years, &c. so that at 6 per cent. one Life is worth above 8 years and a quarter's purchase, two Lives above 12 years and a quarter's pur­chase, &c. as the Table shews.

Now suppose any of those Persons which have their Lives upon an Estate should die, to take in others to make up the Number again, is done by the Table of Reversions at the beginning of the Book: Example, suppose there be three Lives upon an Estate, which at 7 years purchase for the first Life, are valued at almost 12 years purchase, and as a Lease of 27 years, at 7 l. per cent. and if one of those Persons should die, what must be given to make up the Number again? then I say, one Life which is dead was as a Lease of 10 years, and therefore to take in a New Life, I may reckon 10 years of the 27 lapsed, and so take as it were a Fine for renewing

to years lapsed in a Lease of 27 years, now to find this Fine, I take the Summ of the Reversions for 10 years in the Table under 7 l. per cent. counting 27 as 1, 26 as 2, 25 as 3, &c. and so I find the Summ to be 2 l. 4 s. 5 d. 2 q. that is 2 years, and almost one quarters purchase, which I may take for renewing or taking in a New Life; so if two Lives be dead I may reckon 19 years lapsed in a Lease of 27 years, and find the Summ of the Reversions for 19 [Page 21]years, for a Fine for taking in two Lives: but if there be 4 Lives upon the Estate, then at 7 l. per cent. and at 10 years for one Life, they will be reckoned as a Lease of 34 years, and so I must begin at 34 to Summ the Reversions, or at 30 if one Life be reckoned as a Lease of 9 years, and then if one Life be dead, I must reckon 9 years lapsed in a Lease of 30 years, if 2 Lives are dead I must reckon 17 years lapsed in the same Lease, and if 3 are dead I must reckon 24 lapsed: so at 6 l. per cent. reckoning 1 Life as a Lease of 12 years, 3 Lives are as a Lease of 33 years, and so if one of these Lives be dead, I may reckon 12 years lapsed in a Lease of 33 years, if 2 Lives are dead, I may reckon 23 years lapsed in the same Lease, and be­gin at 33 to summ the Reversions, under 6 l. per cent. because the Lives are valued according to the same rate of Interest. This being understood, it will not be diffi­cult to do the like for any other number of Lives, and at other rates of Interest, and number of Years for one Life; for you may by the Table for Purchasing of [Page 22]Leases, &c. make Tables for Purchasing of Lives according to what rate of Interest you think is most convenient; as suppose you reckon one Life as a Lease of 10 years, and you would have 5 l. per cent. profit, then that will be worth 7 years and al­most 3 quarters purchase, but at 8 l. per cent. it is worth but 6 years, and almost 3 quarters purchase, &c.

CHAP. VII.

THE Table for Purchasing is calcula­ted for several rates of Interest, that so the Purchaser may use that which is most convenient for him, as in purchasing of Free-hold Land, 5 l. per cent. may be enough, but for Copy-hold or Leases of Land 6 l. per cent. for Leases of Land and Good Houses 8 l. per cent. and for Leases of Ordinary Houses 10 l. or 12 l. per cent.

The use of the Table is very plain and easy, as by Example will appear, viz.

Example.

What is a Lease or Annuity of 20 years worth at 5, 6, 8, 10, or 12 per cent. per Ann.?

To increase the Number of Years in a Lease, do thus, suppose a Landlord would make a Lease of Land up to 40 years, wherein his Tenant hath 20 years to come, what is it worth? then I say,

Which is the Fine to be given to make the Lease up to 40 years.

To buy a Lease which is not to begin untill your old Lease is out, as thus sup­pose a Man's Lease is out within 4 years, and he desires to have a new Lease of 21 years, to begin when his 4 years are out, what is this Lease worth in ready Money?

For Answer, I add 4 years which is the time he hath in his old Lease, and 21 to­gether, the Summ is 25, then I find the worth of these 25 years, and Subtract from it the Value of the 4 years, the Remain­der is the Value of the said Lease in ready Money.

Example.

CHAP. VIII.

THE use of these Tables aforegoing is easy as by Examples will appear.

The first is this, suppose 30 l. be put out for 20 years, what will it amount unto in that time at 6 per cent. Compound Interest?

Then I look against 20 years, and find under the increase of 1 l. &c. 3 l. 4 s. 2 d. which shews that 1 l. in 20 years time will increase to 3 l. 4 s. 2 d. which I multiply by 30 thus,

that is, 30 l. in 20 years time at 6 per cent. Compound Interest will amount to 96 l. 5 s. 0 d.

The use of the Second is thus, What will an Annuity of 30 l. forborn 20 years amount to in that time? then for Answer I look against 20 years, and under the value of 1 l. Annuity, &c. I find 36 l. 15 s. 8 d. which 36 l. 15 s. 8 d. is the value of 1 l. Annuity forborn 20 years, then I multiply 36 l. 15 s. 8 d. by 30 l. thus,

that is, 36 l. Annuity forborn 20 years will at the end of that term amount to 1103 l. 10 s. 0 d.

The use of the third Table is thus, suppose a Gentleman hath 300 l. by him with which he's willing to purchase an Annuity for 20 years, What Annuity will that purchase at 6 per cent? For Answer I look against 20 years, and find under What Annuity 1 l. ready Money, &c. 1 s. 8 d. 3 q. which shews that 1 l. ready Money will purchase an Annuity of 1 s. 8 d. 3 q. for 20 years, which I multiply by 300 lb. thus,

that is, 300 l. ready Money will purchase an Annuity of 25 l. 18 s. 9 d. for 20 years at 6 per cent.

CHAP. IX. Of the Difference which seems to be, between Long and Short Leases.

SEeing 8 years and an half's purchase is to be given for a Lease of 20 years, at 10 l. per cent. and but 10 years purchase for a Lease of 100 years at the same rate of Interest, that is but for a year and an half's purchase more, to make the Lease 80 years more; it may seem, that he which gives 10 years value for the Lease of 100 years, has abundantly a better Bargain than he which gives 8 years and an half's purchase for the Lease but of 20 years; but then let him consider that in 100 years time his Money is returned but 10 times, whereas in the Lease of 20 years his Money is returned indeed but twice and 3 years over, that is twice in 17 years, but when this Lease is out, he may purchase such another, &c. and so in an 200 years he may receive his purchase Money almost 12 times, but then on the other side let him consider that but 7 of these returns are clear gains, for he gives [Page 34]1 for every 20 years, whereas in the Lease of 100 years he hath 9 returns of his Principal Money clear gains, which con­sideration may still make for the longer Lease to be the best; but then let him that buys this long Lease further consider that although he thinks he gives but little more Money for his 100 years Lease, than he doth, that buys the 20 years Lease, seeing he hath 5 times as many years in his Lease, let him consider I say the increase of his Money for that time, and that he's out of his little Money for a long time; so although he which buys one after another the 5 Leases of 20 years a Lease, is out of a great deal more Money, take them altogether, yet his Money is out but 20 years at a time: from these Considerations it will appear that there is really no difference between a long Lease and a short Lease, if the same rate of Interest in both be observed; for though there may be but little difference between their values, yet the great difference of their term of years will countervalue that, for it is evident that a little Money in a [Page 35]longer time, will amount to as much as a greater Sum in a shorter time: but yet notwithstanding these Considerations I grant there may be other Considerations in which a long Lease may be most profitable to the Tenant, whether it be a Lease of Land or Houses, for if he improves, or repairs, or builds, in a long Lease it is cer­tain, he hath the longer time to enjoy the fruit of his Labour: so a short Lease to the Landlord may be most profitable, or at least most convenient, as for Colleges, &c. who live upon their Fines, and are in continual expence of Money, for them it's certain that a frequent return of Fines is best.