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sold, what is it worth, allowing the buyer 5 per cent for his money

? Ans. 8001, 2. What is an Estate of 2901 per ann. to continue for ever worth in present money, allowing 4 per cent. to the Buyer i Ans. 72501.

CASE 2. Q. When P, and R, are given to find U, how is it discovered :

A. Thus ; ptr-=u

EXAMPLES.

1 If a Freehold Estate is bought for 8001 and the allowance of 5 per cent. is made to the buyer; I demand the yearly rent? Ans. 40l per ann.

2 If an estate be sold for 7250l present money, and 4 per cent. is allowed to the buyer for the same; I demand the yearly rent? Ans. 2901 per ann.

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

p+u A. Thus : р

EXAMPLES. I If a real estate of 401 per ann. be sold for 800l. I demand the rate per cent. ? Ans. 5 per cent.

2 If a Freehold Estate of 2901 per ann. be bought for 72501. I demand the rate per cent. allowed ? Ans. A per. cent. OF PURCHASING FREEHOLD ESTATES IN

REVERSION.

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, to do which there are given T, and R, to find P.

Q. How is P discovered ?

u

A. Thus :

-

1 Q. What is the second operation? A. Find what principal being put to interest will go

wount to P at the same rate, and for the time to come before the estate commences, and that will be the present worth of the estate in Reversion : therefore let P be changed into A=the amount and then there will be given A, R and T, to find P=the principal.

Q. How is P discovered ?

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EXAMPLES.

1. Suppose a Freehold Estate of 401. per ann. to commence 3 years hence, is to be sold, what is it worth, allowing the purchaser 5 per cent. for his present payment P Ans. 6911 is 4d 3 qrs.to

2. What is an estate of 2901 per ann. to continue for ever, but not to commence till the expiration of 4 years, worth in present money, allowance being made at 4 per cent? Ans. 61971 6s 5d 2 qrs. +

CASE 2.
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 rent, at the given rate, and for the time before the estate commences; to do which there are given P, T, and R, to find A. Q. How is A discovered ?

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

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

Q. How is U discoverd ?

r

prtrapr A. Thus %

EXAMPLES. 1. suppose a Freehold Estate, to commence 3 years hence, is sold for 6911. Is 5d. allowing to the purchaser 5 per cent. I demand the yearly income? Ans. 401 per annum.

2. There is a certain Freebold Estate bought for 6197% 68 5d 2-qrs. which does not commence till the expiration of 4 years; the buyer was allowed 4 per cent. for his money; I demand the yearly income? Answ. 2901, per an

num.

OF REBATE OR DISCOUNT.
Q. What particular Letters are used here?
A. These;
S. the sum to be discounted for.

P. the present worth of that sum, due at any time to come.

T. the time before it becomes due, and
R. the amount of 11 for a year, at any rate per cent.

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

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EXAMPLES. 1. What is the present worth of 5201 188 58 2 qrs payable 3 years hence, at 5 per cent ? Ans. 4:01

2 There is a debt of 5041 19s 9d 3qrs. which is not due until 4 years hence : but it is agreed to be paid in present money; wbat sum must the Creditor receive; allowing the Rebate of 6 per cent to the Debtor for his money ? Ans. 4001.

3 If 6431 48 11d payable in 6 years time, what is the present worth, Rebate being made at 5 per cent ? Ans. 4801.

CASE 2. Q. When P, T, and R, are given to find 8, how is it discovered ?

t

A. Thus; p+ros

EXAMPLES.

1. If 450l be received for a debt, payable 3 years hence, and an allowance of 5 per cent. was made to the debtor for his present payment; I demand what the debt was? Ans. 5201 18s 7d 2qrs.

2 There is a sum of money, due at the expiration of 4 years, but the Creditor agrees to take 4001 down, als

lowing 6 per cent. on present payment: I demand what the debt was ? Ans. 5041 19$ 9d 3qrs. 2 If a sum of money,

due 6

years hence produces 4801 for present payment. Rebate being made at 5 per cent. I demand how much the debt was ? Ans. 6431 4s lid.

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

which being continually divided A. Thus 3

by r,till nothing remains the numр

ber of those divisors will be=t.

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t

EXAMPLES.

I A certain man received 4501 dowy, for a debt of 4201 188 7d 2qrs. Rebate being at 5 per cent. I demand in what time the debt was payable ? Ans. 3 years.

2 There is a debt of 504 19s 9d 3qrs. payable at a certain time; but it is agreed to pay 4001 down, at the allowance of 6 per cent to the debtor for his present money: 1 demand in what time the debt will become due, if no such payment was to be made ? Ans. 4 years.

3 The present payment of 4801 is made for a debt of 6431, 45 ild Rebate at 5 per cent. I demand when the debt was payable ? Ans. 6 years.

CASE 4. Q. When S, P, and T, are given to find R, how is it discovered?

t which must be extracted by the rules A. Thus;

of extraction; the time given in the р

questions=t, shewing the power.

S

EXAMPLES.

1 The present worth of 5201 18s 7d 2qrs. payable 3 years hence, is 4501 I demand at what rate per cent. Rebate is made ? Ans. 5 per cent.

2 A debt of 5041 198 9d 3qrs will be due 4 years hence ; but it is agreed to take 4001 down; what is the rate per cent. that the Rebate is made at ? Ans. 6 per cent.

3 The sum of 6431 4s i id is payable in 6 years time; and the present worth of that sum is 4801 I demand at what rate per cent. must Rebate be made, to produce the said present worth ? Ans. 5 per cent.

Note 1. Equation of Payments at Compound Interest, should follow next; but as that rule is best done by the Logarithms, the kind reader will, I hope, take this as a sufficient reason for not plac-ing it here.

2. The whole business of Compound Interest, is better performed by the Logarithms, or by Tables calculated for that purpose, than otherwise ; especially when the time given is very long, as 20, 30, or 40 years, and when the payments are to be made half-yearly or quarterly. What is here done serves only for whole years, and shews what can be done by the pen, where the Logarithms or tables are wanting

A practical and easy Method to cast up the Value of Timber. Rule. Multiply the Number of Feet by the Price (in Shillings) per Load, and cut off 3 places to the right hand, which makes pouds and Decimal Parts thereof.

EXAMPLES.

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754 Feet at 1178 6d per Load, 856 Feet at ll 6s per load 754 754 at 6d.=377

Facit 221 5s 1d1 27

730 Feet at 11 8s od

per

load.

Facit 201 16s id 20358

433 feet at ll 3s 6d

per

load. +377

Facit 10i 3s 6d 1. d. 20.735=20 14 91

Demonstration. 50 Feet make a Load; therefore it is, as 50 Feet . Price in Shillings :: Feet given.. Value in Sbillings, which 20 are Pounds: But as 50x20=1000 which is a Divisor for Pounds ; therefore the first figure being 1, a d the rest Cyphers. Division is made at once, by pointing off three places as above.

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