sold, what is it worth, allowing the buyer 5 per cent for his money? Ans. 8001,

2. What is an Estate of 290l per ann. to continue for ever worth in present money, allowing 4 per cent. to the Buyer Ans. 72501.

CASE 2.

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

A. Thus; p+r-1=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. 40/ 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. 290l per ann.

CASE 3.

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

1 If a real estate of 401 per ann. be sold for 8001. I demand the rate per cent. ? Ans. 5 per cent.

2 If a Freehold Estate of 290l per ann. be bought for 72501. I demand the rate per cent. allowed? Ans. 4 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 U, and R, tó find P.

Q. What is the second operation ?

A. Find what principal being put to interest will &

mount 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.

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 ? Ans. 6917 Is 4d 3 qrs.+

2. What is an estate of 290l 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. 61977 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 year ly 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; pr=α

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 Ự, or the yearly sum.

Q. How is U discoverd ?

1. suppose a Freehold Estate, to commence 3 years hence, is sold for 691. 1s 5d. allowing to the purchaser 5 per cent. I demand the yearly income? Ans. 40 per

annum.

2. There is a certain Freehold Estate bought for 6197 6s 5d 2qrs. 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. 290l. 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?

A. Thus ;

S

t

EXAMPLES.

1. What is the present worth of 5201 18s 5d 2 qrs payable 3 years hence, at 5 per cent? Ans. 450l

2 There is a debt of 5041 19s 9d 3qrs. which is not due until years hence but it is agreed to be paid in present money; what sum must the Creditor receive; allowing the Rebate of 6 per cent to the Debtor for his money ? Ans. 400l.

3 If 6431 4s 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?

A. Thus; p+r=s

EXAMPLES.

1. If 450l be received for a debt, payable S 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. 520l 18s 7d 2qrs.

2 There is a sum of money, due at the expiration of 4 years, but the Creditor agrees to take 400 down, al

lowing 6 per cent. on present payment: I demand what the debt was? Ans. 504/ 19s 9d 3qrs.

2 If a sum of money, due 6 years hence produces 480/ for present payment. Rebate being made at 5 per cent. I demand how much the debt was ? Ans. 643/ 4s 1d.

CASE 3.

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

1 A certain man received 450l down, for a debt of 4201 18s 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 400 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 480l is made for a debt of 643 4s d 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?

1 The present worth of 520l 18s 7d 2qrs. payable 3 years hence, is 450 I demand at what rate per cent. Rebate is made? Ans. 5 per cent.

2 A debt of 504/ 19s 9d 3qrs will be due 4 years hence; but it is agreed to take 400/ down; what is the rate per cent. that the Rebate is made at ? Ans. 6 per cent.

3 The sum of 643 4s id is payable in 6 years time; and the present worth of that sum is 480 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 placing 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 pounds and Decimal Parts thereof.

EXAMPLES.

754 Feet at 177s 6d per Load, 856 Feet at 17 6s per load 754 at 6d.377 Facit 221 58 1d

754
27

20358 +377

1. S. d. 20.735=20 14 91

730 Feet at 11 8s od per load. Facit 20/ 16s id 433 feet at 1/ 3s 6d per load. Facit 101 3s 6d

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