RULE.

As 100+ interest of $100 for the given time, is to 100, so is the face of the note to its present value.

EXAMPLES.

1. What is the present value of a note for $1828,75 due in one year, at 4 per cent per annum?

100

4,50 interest of $100 for the time.

104,50 100 :: 1828,75 : Ans.

100

104,50)182875,00($1750.

Ans. $1750.

2. What is the present value of a note for $1290,81 discounted for four months, at 6 per cent per annum? Ans. $1265,50. 3. What is the present value of $800, due 4 years hence the interest being computed at 5 per cent per annum? Ans. $666,66 6+

NOTE. When payments are to be made at different times, find the present value of the several sums separately and their sum will be the present value of the note.

1. What is the present value of a note for $3500 on which $300 are to be paid in 6 months; $900 in one year; $1300 in eighteen months; and the residue at the expiration of two years: the rate of interest being 6 per cent per annum? Ans. $3225,83+. 5. What is the discount of £1500 one-half payable in 6 months and the other half at the expiration of a year, at 7 per cent per annum? Ans. £

+

6. What is the present value of $2880, one-half payable in 3 months, one-third in 6 months, and the rest in 9 months at 6 per cent per annum? Ans. $2810,08+

Q. What is the face of a note? What is the present value of a note? What is the discount of a note? How do you find the present value of a note? When payments are to be made at different times, how do you find the present value?

LOSS AND GAIN.

§ 165. Loss and Gain is a rule by which merchants discover the amount lost or gained in the purchase and sale of goods. It also instructs them how much to increase or diminish the price of their goods so as to make or lose so much per cent.

EXAMPLES.

1. Bought a piece of cloth containing 75yd. at $5,25 per yard, and sold it at $5,75 per yard: how much was gained in the trade?

2. Bought a piece of calico containing 50yd. at 2s 6d per yard: what must it be sold for per yard to gain £1 Os 10d?

3. Bought a hogshead of brandy at $1,25 per gallon, and sold it for $78: was there a loss or gain?

Ans. loss of $0,75.

4. A merchant purchased 3275 bushels of wheat for which he paid $3517,10, but finding it damaged is willing to lose 10 per cent: what must he sell it for per bushel?

Ans. $0,96+.

5. A bought a piece of cotton containing 40 yards, at 6 cents per yard; he sold it for 7 cents per yard: how much did he gain? Ans. $0,60. 6. Bought a piece of cloth containing 75 yards for $375: what must it be sold for per yard, in order to gain $100? Ans. $6,33 per yard.

7. Bought a quantity of wine at $1,25 per gallon, but it proves to be bad and am obliged to sell it at 20 per cent less than I gave: how much must I sell it for per gallon? Ans. $1 per gall.

8. A farmer sells 125 bushels of corn for 75cts. per bushel; the purchaser sells it at an advance of 20 per cent: how much did he receive for the corn? Ans. $

9. A merchant buys one tun of wine for which he pays $725, and wishes to sell it by the hogshead at an advance of 15 per cent: what must he charge per hogshead?

Ans. $208,43+.

10. A merchant buys 158 yards of calico for which he pays 20 cents per yard; one-half is so damaged that he is obliged to sell it at a loss of 6 per cent; the remainder he sells at an advance of 19 per cent: how much did he gain? Ans. $2,05+.

EQUATION OF PAYMENTS.

§ 166. I owe Mr. Wilson $2 to be paid in 6 months; $3 to be paid in 8 months; and $1 to be paid in 12 months. I wish to pay his entire dues at a single payment, to be made at such a time, that neither he nor I shall lose interest at what time must the payment be made?

The method of finding the mean time of payment of several sums due at different times, is called Equation of payments.

Taking the example above. Int of $2 for 6mo. " of $3 for 8mo. " of $1 for 12mo.

9$

int. of $1 for 12mo. 2x 6=12 int. of $1 for 24mo. 3× 8=24 int. of $1 for 12mo.

48

1x 12=12

48

The interest on all the sums, to the times of payment, is equal to the interest of $1 for 48 months. But 48 is equal to the sum of all the products which arise from multiplying each sum by the time at which it becomes due: hence, the sum of the products is equal to the time which would be necessary for $1 to produce the same interest as would be produced by all the sums.

Now, if $1 will produce a certain interest in 48 months, in what time will $6 (or the sum of the payments) produce the same interest. The time is obviously found by dividing 48, (the sum of the products,) by $6, (the sum of the payments.)

Hence, we have the following

RULE.

Multiply each payment by the time before it becomes due, and divide the sum of the products by the sum of the payments: the quotient will be the mean time.

2. B owes A $600: $200 is to be paid in two months, $200 in four months, and $200 in six months: what is the mean time for the payment of the whole?

3. A merchant owes $600, of which $100 is to be paid in 4 months, $200 in 10 months, and the remainder in 16 months if he pays the whole at once, at what time must he make the payment? Ans. months. 4. A merchant owes $600 to be paid in 12 months, $800 to be paid in 6 months, and $900 to be paid in 9 months: what is the equated time of payment. Ans. 8mo. 22da

5. A owes B $600; one-third is to be paid in 6 months, one-fourth in 8 months, and the remainder in 12 months: what is the mean time of payment? Ans. 9 months.

6. A merchant has due him $300 to be paid in 60 days, $500 to be paid in 120 days, and $750 to be paid in 180 days: what is the equated time for the payment of the whole? Ans. 137 days.

7. A merchant has due him $1500; one-sixth is to be paid in 2 months; one-third in 3 months; and the rest in 6 months: what is the equated time for the payment of the whole? Ans. 43 months.

NOTE. If one of the payments is due on the day from which the equated time is reckoned, its corresponding product will be nothing, but the payment must still be added in finding the sum of the payments.

8. I owe $1000 to be paid on the 1st of January, $1500 on the 1st of February, $3000 on 1st of March, and $4000 on the 15th of April: reckoning from the 1st of January, and calling February 28 days, on what day must the money be paid?

Ans. Payment in 6714 days, or on the 8th March.

Q. What is Equation of Payments? What is the sum of the products which arise from multiplying each payment by the time to which it becomes due equal to? How do you find the mean time of payment? When you reckon the time from the date at which the first payment becomes due, do you include the first payment?

FELLOWSHIP.

§ 167. Fellowship is the joining together of several persons in trade with an agreement to share the losses and profits according to the amount which each one puts into the partnership. The money employed is called the Capital Stock.

The gain or loss to be shared is called the Dividend. It is plain that the whole stock which suffers the gain or loss must be to gain or loss, as the stock of any indiviqual to his part of the gain or loss.