(50) The Sum of 7431 4s 9d is payable in 6 Years' Time, and the present Value of that Sum is 5871 7s 03d, I demand at what Rate per Cent. the Rebate must be inade?

LXXII. PURCHASING FREEHOLD or REAL

ESTATES

IS to find the present Worth of an Annuity, &c. to continue

(51) Suppose a Freehold Estate of 500/ per Annum were to be sold,; what is the Worth, allowing 5 per Cent. to the Buyer?

(52) What is an Estate of 25 per Annum, to continue for ever, worth in present Money, allowing 44 per Cent. to the Buyer?

When P and U are given, to find 3.

(53) Suppose one gave 10000 for a Freehold Estate of 500/ per Annum, what Rate per Cent. has the Purchaser for his Money?

(54) If an Estate of 251 per Annum is bought for 555/ 11s 14d. what is the Rate per Cent?

When P and R are given, to find U.

THEOREM 22. P+r—1=U.

EXAMPLES.

(55) Suppose a Person would lay out 10000/ on a Freehold

Estate, and so as to be allowed 5 per Cent. for his
Money, what must be the Annual Rent of such an
Estate?

(56) If a Freehold Estate is bought for 5551 11s 1d. and the Allowance of 44 per Cent. is made to the Buyer, what is the Yearly Rent?

LXXIII. PURCHASING FREEHOLD ESTATES in REVERSION.

To find the Worth of a Freehold Estate in Reversion.

RULE.

น

1. Find the Worth of the THEOREM 23. Thus---P. Yearly Rent, &c.

2. Change P into A, and find what Principal being put to Interest will amount to A, at the same Rate, and for the Time to come before the Estate commences.

A
Thus--P.

EXAMPLE.

Rt.

(57) What is an Estate of 500/ per Annum worth in ready Money, to continue for ever, but not to commence till the End of 4 Years, allowing 5 per Cent. to the Purchaser?

To find the Yearly Rent of an Estate taken in Reversion.

RULE.

1. Find the Amount of the THEOREM 24. pxr=A. Worth of the Estate at the

given Rate, and the Time

before it commences.

2. Change A into P, and find Prxr-pr

what Yearly Rent being

sold will produce P at the

same Rate.

= Մ.

r

EXAMPLES.

58) A Freehold Estate is sold for 82271 1s 4d. which does not commence till the End of 4 Years, the Buyer being allowed 5 per Cent. for his Money: I desire to know the Yearly Income?

QUESTIONS for Exercise.

(59) Held of a College 486 10s a-Year, on a reserved Rent of 941. Money being at 5 per Cent. Interest;

what Fine ought severally to be paid on a 7, a 14,

and a 21 Years' Lease?

(60) Suppose I would add 5 Years to a running Lease of 15 Years to come, the improved Rent being 186/ 7s 6d per Annum; what ought I to pay down in ready Money for this Favour, discounting 4 per Cent.? (61) A has a Term of 7 Years in an Estate of 50/ per Annum; B hath a Terin of 14 Years in the same Estate; and C hath a further Term of 10 Years after B in the same Estate. What is the present Value of the several Interests in the said Estate?

(62) For a Lease of certain Profits for 7 Years, A offers to pay 150/ Gratuity, and 300/ per Annum; B offers 400/ Gratuity, and 250/ per Annum; C bids 650/ Gratuity, and 2007 per Annum; and D offers 1800/ for the whole Purchase, without any Yearly Rent. Quere, which is the best Offer? and what Difference computing at per Cent.?

(63) Value the Lease of a House in tolerable Repair, the Rent 54/ 17s a Year, the Ground Rent 7 Guineas; 3 Years of it only to come; the Rent payable every 6 Months; Discount per Compound Interest on this Kind of Purchase at 10 per Cent. ?

(64) A Fine for a Lease of a Tenement is settled at 1531. under a reserved Rent of 16/ a-Year. Now the Tenant cannot conveniently pay more than 50%; but, for the 6 Years to come of the Term, is willing rather to pay an adequate Rent, computing 107 per Cent. per Conpound Interest. What ought that Rent to be? (65) Another Lease for 7 Years is agreed for at 250l. Fine, on the old Rent, 441. a Year; but considering the Contractor desires to reduce the Rent to 20/ a-Year, and pay a proper Fine, computing as before, after the Rate of 10/ a-Year; to what must the Fine be advanced?

(66) A Son, previous to his Marriage, is minded to have 50/ a-Year Freehold settled c. bis Family; and, to have immediate Possession of it, offers his Father, in Lieu, an Annuity for his Life, Valued at 12 Years'

Purchase, discounting at 4 per Cent: thereon: whereas he is content the Estate should be valued at a Discount of 3 per Cent. and consequently will be worth 33 Years' Purchase. Pray what had the Father for his Life?

(67) A Gentleman took a College Lease of 237/ a-Year, for 21 Years, and paid the full Fine; the Rent reserved was 107 a-Year; but when 4 Years were clapsed against the Marriage, he renewed the Lease, and filled up the 21 Years. In 14 Years after that, his Wife dying, he again renewed it in Favour of his Daughter, then 7 Years of Age; and by the Time she was 19, it was a third Time renewed, in order to her Settlement. The Question is, what Money the Society must have received from this Family from first to last allowing 5/ a-Year Discount on the Fines?

THE

TUTOR'S GUIDE. A

PART IV.

LXXIV. MENSURATION.

GEOMETRICAL DEFINITIONS.

GEOMETRY contains the Nature and Properties of

Lines, Angles, Surfaces, and Solids.

A Point is that which has no Parts or Magnitude.
A Line is Length conceived without Breadth.

An Angle is the mutual Inclination of two Lines which

meet.

When a straight Line, as CD, (Fig. 4.) standing upon another, A B, makes the Angles, A D C, and C D B, on oach Side equal to one another, each of these equal Angles is called a right Angle, and the dotted Line, C D, is said to be perpendicular to the Line A B.

An Angle is commonly expressed by three Letters, that placed at the Angular Point being always wrote in the Middle, as ADC (Fig. 4. denotes the Angle b.

An Obtuse Angle is that which is greater than a right Angle, as C A B, (Fig 3.)

An acute Angle is that which is less than a right Angle, as D C B, (Fig. 4.)

Parallel Lines are those of which every Point of the one is at the same Distance from the other, as the Lines A B and CD, (Fig. 2.)