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40l per ann. amount to 3351 158 11d. at 6 per cent. for non-payment? Ans. 7 years.

4 İn what time will a salary of 351 per ann. amount to 2411 1s 7d 2.6 qrs. at 5.1 per cent for the forbearance of payment ? Ans. 6 years.

Note. In this and the two next Sections might be placed Case 4 ; but because it requires an algebraic method of proceeding, in order to find R, I omit inserting it in its place; this being designed to treat only of numbers. OF THE PRESENT WORTH OF ANNUITIES,

PENSIONS, &c.
Note. P, is the present worth, U, T, and R, as in the last.

CASE 1. Q. When U, T, and R, are given to find P, how is it discovered ?

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EXAMPLES.

1. What is the yearly rent of 201 to continue 6 years, worth in ready money, at 5 per cent ? Ans. 1011 lus 3d. 3qrs.

2 What is the present worth of a pension of 301 per ann. for 5 years at 4 per cent? Ans. 133' ils ld.

3 What must be the discount of a lease of 50l per ann. when present payment is made for 4 years at 3 per cent ? Ans. 141 2s 10d 2qrs.

4 A house is let upon lease for 4 years, at 70l per ann. and the lessee is desirous to make present payment, provided the lessor will allow him 5 per cent.' I demand how much must be paid down, and how much discounted ?

2431 19s Od 3qrs to be paid down.
Ans.
361 Os Ild Iqr to be discounted.

OASE 2. Q. When P, T, and R, are given to find U, how is it discovered ?

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EXAMPLES.

1 What annuity or yearly rent, to continue 6 years may be purchased for 1011 10s 3d 3qrs at 5 per cent ? Ans. 201

2 Suppose the present payment of 1331 11s Id were required for a pension for 5 years to come, at 4 per cent. what is that pension ? Answer 301 per ann.

3 If the present payment of 1857 178 1d 2qrs. be made for the lease of a house, 4 years to come, at 3 per cent. is hat is the yearly rent? Answer 50l per annum.

4 If a house is let upon lease for 4 years, and the lessee makes present paymeut of 2431 19s Od 3qrs for that iiine at 5 per cent. what is the yearly rent of the house? Ans. 701 per

CASE 3. Q. When U, P, and R, are given to find T, how is it discovered ?

which being continually divid

ed by r, till nothing remains, A. Thus ;

the number of those divisions ptumpr

will be=t.

ann.

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EXAMPLES

1 How long may a lease of 201 yearly rent be had for 1041 108 3d 3qrs allowing 5 per cent to the purchaser? Answer 6 years.

2 I demand what time a lease of 301 per annum may be parehased for; when present payment of 133! 11s 1d is inade at 4 per cent ? Answer 5 years.

3 If 1851 17s 1d 2qrs. be paid down for a lease of 501 per annum at 3 per cent. how long is the lease purchased for? Answer 4 years.

4 A house is let upon lease, at 701 per annum and the lessee makes present payment of 2431 19s 0d 3qrs he being allowed 54 per cent. I demand how long the lease is purchased for? Answer 4 years. OF ANNUITIES, LEASES, &c. TAKEN IN REVER:

SION.

CASE 1.
Q. How many operations are there in Case 1:
A. Two.
Q. What is the first?

A. Find the present worth of the yearly sum at the given rate, and for the given time of its continuance; to do which there are given U, T, and R, to find P.

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A. Thus ;

pl Q. What is the Second ?

A. Find what principal being put to interest will amount to P, at the same rate, and for the time to come before the annuity commences, and that will be the present worth of the annuity, &c. In Reversion ; therefore let P be changed into Athe amount, and then there will be given A,. R, and T, to find P, or the Principal.

Q. How is P discovered ?

a

A. Thus ;

t

EXAMPLES:

1 What is the present worth of the Reversion of a Lease of 201 per ann. to continue 4 years, but not to commence till the end of two years, allowing 5 per cent to the purchaser ? Ans. 641 6s 6d 1.4+qrs.

2 There is a lease of certain lands worth 32l per ann. which is yet in being for 4 years ; and the Lessee is desirous to take a Lease in Reversion for 7 years, to begin when the old Lease shall be expired; I demand the present worth of the said Lease in Reversion, allowing 5 per cent to the purchaser ? Ans. 1521 6s 8d 2grs+.

3 There is a house now building, which I have a-mind to take a Lease of for 8 years ; but the house will not be finished within two years : 1 demand how much I must pay down, when the yearly rent is 1001 and the landlord allows me 4 per cent on present payment ? Ans. 6221 95 7.22

Q. How many operations are there in Case 2
A. Two.
Q. What is the first ?

A Find the amount of the present worth of the yearly sum at the giren rate, and for the time before the ana nuity commences, to do which there are given P, R, and r, to find A.

CASE 2.

Q. How is A discovered ?

t A. Thus pr=a Q. What is the second ?

A. Find what yearly rent being sold will produce A for the present worth at the same rate, and for the time of its continuance; and that will be the yearly sum required: therefore let A be changed into P, and then there will be given P, R, to find U, or the yearly sum.

t
A. Thus; prxn--pr

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EXAMPLES.

i What annuity or yearly rent to be entered upon 2 years hence, and then to continue 4 years, may be

purchased for 641 6s 6d 2qrs ready money, at 5 per cent. ? Answer 201.

2 There is a Lease of certain lands in being for 4 years, and the Lessee being minded to take a Lease in Reversion for 7 years, to begin when the old Lease shall he expired, laid down 1521 68 8d 2qrs. I demand the yearly rent of the said lands, when allowance was made to the Lessee, at 5 per cent ? Ans. 32l per ann.

3 The present payment for the Lease of a house is 6221 9s 7.2d. Now I bave taken a Lease in Reversion for 8 years, which is to commence at the end of two years ; I demand how much the yearly rent is, when for The said present payment I was allowed 41 per cent ? Ans. 1001 per ann.

CASE 3.
Q. How many Operations are there in Case 3
A. Two.
Q. What is the First ?

A. Find the aniount of the present worth of the yearly sum at the given rate, and for the time before the annuitý, d.c. eommences ; to do whieh there are given P, R, and T, to find A, as in Case 2. Q. How is A discovered ?

t A. Thus : prsa Q. What is the second operation?

A. Find what time the yearly rent given being sold for will produce A for the present worth, at the same rate, and iliat will be the time required : therefore change A into P, and then therë will be given W, P, and R, to find T, as in Case 3, page 164. Q. How is T discovered ?

which being continually di

vided by r till nothing rèA. Thus 3

mains, the Number of those p+u-pr Divisions will be=t.

u

EXAMPLES.

1 The present worth of a certain Lease in Reversion is 641 6s 6d 2qrs the Lease is 20l per annum and commences 2 years hence, and the allowance to the purchaser is 5 per cent. I demand the time of its continuance? Answer 4 years.

2 A certain man took à Lease of some Lands, for a time, which by agreement was not to commence till the expiration of 4 years ; the yearly rent was 321 it was also agreed, that the purchaser should lay down 1521 68 3d 2 qrs.

and be allowed for his present pay at 5 per cent. I demand the time that the Lease was taken for? Answer 7 years.

3 The present payment for the Lease of a house is 6221 9s 7.2d. and the yearly rent is 1vol. Now I have taken a lease in reversion, which is to commence at the end of two years; I demand the length of the lease, when I was allowed 4 per cent. for my Money? Answer 8 years.

OF PURCHASING REAL OR FREEHOLD ESTATES. Q. What do yon understand by a Real or Freehold estate ?

A. Such as is bought to continue for ever.

Note. U represents the yearly rent; R, the amount of 11. &c. and P the present worth.

CASE 1. Q. When U, and R, are given to find P, how is it discovered? A. Thus ;

=P

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EXAMPLES.

i Suppose a Freehold Estate of 40l per annüm is to be

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