Arithmetic Designed for Academies and Schools

RULE.

As 100+ interest of $100 for the given time, is to 103, 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+.

II. Then find the interest as though the sum were dollars and cents; after which reduce the decimal part of the answer to shillings and pence (see § 137).

EXAMPLES.

1. What is the interest, at 6 per cent, of £27 15s 9d for 2 years?

2. What is the interest on £67 for 3 years 8 months 16 days?

3. What is the interest on £127

for 3 years and 3 months?

1,120000

Ans. £3 6s 84d+

19s 6d, at 6 per cent, Ans. £15 2s 81⁄2d+. 15s 4d, at 6 per cent, Ans. £24 18 31d+. 16s 10d, at 6 per cent,

4. What is the interest of £107 for 3 years 6 months and 6 days? Ans. £

5. What will £279 13s 8d amount to in 3 years and a

half, at 54 per cent per annum?
6. What is the interest of £514

a half, at 4 per cent?

7. What is the interest of £523

a half, at 6 per cent?

8. What is the interest on £255 per annum, for 6yr. 6mo.?

Ans. £331 1s 6d+. 10s 2d for 3 years and

Ans. £72 0s 71d+. 11s 6d for 3 years and Ans. £ +. 10s 8d at six per cent Ans. £99 13s 1d.

9. What is the interest on £53 18s 5d at 6 per cent for 7yrs, 12da.?

Ans. £22 15s ld+.

APPLICATIONS.

Calculate the interest on the following notes.

$127,50

New York, January 1st, 1838.

1. For value received I promise to pay on the 10th day of June next, to Wm. Johnson or order, the sum of one hundred and twenty-seven dollars and fifty cents with interest from date, at 7 per cent. John Liberal. Ans. $131,46+.

$306

New York, January 1st, 1833.

2. For value received I promise to pay on the 4th of July, 1835, to Wm. Johnson or order, three hundred and six dollars with interest at 6 per cent from the 1st of March, 1833. John Liberal. Ans. $349,04+.

$1040

Hartford, July 3rd, 1837.

3. Six months after date, I promise to pay to C. Jones or order, one thousand and forty dollars with interest from the 1st of January last, at 7 per cent. Joseph Springs. Ans. $1113,40+.

§ 160. We shall now give the rule established in New York, (See Johnson's Chancery Reports, Vol. I. page 17,) for computing the interest on a bond or note, when partial payments have been made. The same rule is also adopted in Massachusetts, and in most of the other states.

RULE.

I. Compute the interest on the principal to the time of the first payment, and if the payment exceed this interest, add the interest to the principal and from the sum subtract the payment: the remainder forms a new principal.

II. But if the payment is less than the interest, take no notice of it until other payments are made, which in all, shall exceed the interest computed to the time of the last payment: then add the interest, so computed, to the principal, and from the sum subtract the sum of the payments: the remainder will form a new principal on which interest is to be computed as before.

EXAMPLES.

$349,99 8.

May 1st, 1826.

1. For value received I promise to pay James Wilson or order, three hundred and forty-nine dollars ninety-nine cents and eight mills with interest, at 6 per cent.

James Paywell.

On this note were endorsed the following payments: Dec. 25th, 1826 Received $49,998

July 10th, 1827
Sept. 1st, 1828

June 14th, 1829