thousandths of a pound. And £75.775 × .162=£12.27555 £12. 5s. 6.132d., the interest required.

69. What is the interest of £25. 18s. 9d. for 10 months and 15 days, at 6 per cent. a year?

Ans. £1. 7s. 2d. 3qrs.+. 70. What will be the interest of £45. 12s. 6d. from January 1st, 1847, to July 16th, 1847, at 6 per cent. a year? 71. What will be the interest of £500 from January 20th, 1847, to September 20th, 1847, at 6 per cent. a year? What will be the amount?

Art. 147. Since the interest of 1 dollar for any given number of days is one sixth as many mills as there are days, it follows that the interest of any given number of dollars for any given number of days must be equal to one sixth of the product of the number of dollars multiplied by the number of days, in the denomination of mills. Hence the following rule for computing interest for any number of days.

RULE. Multiply the given sum or number of dollars by the given number of days, divide this product by 6, the quotient will be the interest in mills, when the sum is dollars only; but when there are cents in the given sum, the quotient will be the interest in hundredths of mills.

72. What is the interest of $25 for 25 days?

Åns. $.104+.

73. What is the interest of $10 for 10 days?

Ans. $.016.+

74. What is the interest of $15 for 15 days?

Ans. $.037+.

75. What is the interest of $75 for 33 days?

Ans. $.412+.

76. What is the interest of $100 for 63 days?

Ans. $1.05+.

77. What is the interest of $125 for 93 days?
78. What is the interest of $24.75 for 20 days?
79. What is the interest of $45.15 for 35 days?
80. What is the interest of $75.25 for 45 days?
81. What will be the interest of $175.75 for 33 days?
82. What will be the interest of $525.25 for 63 days?

In the above method of computing interest for days, the year is supposed to contain 360 instead of 365 days; hence, the interest found for any given number of days will be too large by its part, by which it must be diminished when perfect accuracy is required.

PARTIAL PAYMENTS.

Art. 148. WHEN partial payments have been made and endorsed upon notes and bonds, the following rule has been adopted by the Supreme Court of the United States, also by the Courts in Massachusetts, New York, and by the Courts in most of the other States, for computing the interest. It is given in the language of Chancellor Kent, of New York.

"The rule for casting interest, when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due.

66

"If the payment exceeds the interest, the surplus goes towards discharging the principal, and the subsequent interest is to be computed on the balance of principal remaining due. If the payment be less than the interest, the surplus of interest must not be taken to augment the principal; but interest continues on the former principal until the period when the payments, taken together, exceed the interest due, and then the surplus is to be applied towards discharging the principal; and interest is to be computed on the balance, as aforesaid."

83.

$1250.00.

Boston, January 1st, 1846. For value received, I promise to pay William Briggs, or order, twelve hundred and fifty dollars on demand, with interest at 6 per John Smith.

cent.

The following payments were endorsed on this note.
April 1st, 1846, received $175.75.
August 1st, 1846, received $20.00.
November 1st, 1846, received $360.00.

W. Briggs.

W. Briggs.

W. Briggs.

January 1st, 1847?

$1250.00.

$157.00.

$1093.00.

$380.00.

$38.255.

$341.745.

$751.255.

7.51255.

$758.76755.

What was the amount due on this note
Principal, January 1st, 1846,
First payment, Jan. 1st, 1846, $175.75.
Interest to first payment (3 mo.) $18.75.
Excess of payment above the interest,
Principal or sum due after first payment,
Second payment, Aug. 1st, 1846, $20.00,
Third payment, Nov. 1st, 1846, $360.00,
Interest to Aug. 1st, 1846, (4 mo.) $21.86,
Interest to Nov. 1st, 1846, (3 mo.) $16.395,
Excess of the payments above the interest,
Principal or sum due after the third payment,
Interest to January 1st, 1847, .

Amount due on note January 1st, 1847,

The day on which the note is dated, and the day on which it falls due, are not both reckoned in determining the time, but one of them is always excluded.

84.

$775.00.

Lowell, March, 15th, 1846.

For value received, I promise to pay C. D. on demand, seven hundred and seventy-five dollars, with interest.

This note is endorsed as follows:
June 1st, 1846, received $25.00.
Sept. 15th, 1846, received $45.75.
Dec. 1st, 1846, received $75.00.
May 15th, 1847, received $200.00.
What will be due Sept. 1st, 1847 ?
85.

$550.00.

A. B.

C. D.

C. D.

C. D.

C. D.

Ans. $487.98+.

Worcester, January 25th, 1846. For value received, we, jointly and severally, promise to pay J. R., or order, five hundred and fifty dollars, in three months from date, with interest after three months.

W. P.

S. L.

The following payments are endorsed on this note :
July 20th, 1846, received $75.25.
Sept. 25th, 1846, received $50.75.
Dec. 20th, 1846, received $45.50.

J. R.

J. R.

J. R.

What was due on this note January 25th, 1847?

86.

$1200.00.

Ans. $400.02+.

Salem, June 10th, 1846.

For value received, I promise to pay A. B., or bearer, twelve hundred dollars on the 1st day of January, 1847, with interest from date.

J. P.

Suppose the following payments to have been endorsed on this note, what was due January 1st, 1847 ?

For value received, I promise to pay T. P., or order, fifteen hundred dollars on demand, with interest.

G. B. C. Suppose $200 to have been paid on this note on the first day of August, September, October, November, and December, what was due on the 1st of January, 1847?

Art. 149. The following rule is sometimes used for computing the interest on bonds and notes, upon which partial payments have been made.

RULE. Compute the interest on the note from the time the interest commenced to the time of settlement, and find the

amount.

Then compute the interest on each payment from the time it was paid to the time of settlement, and find the amount of each. Lastly, deduct the total amount of the several payments from the amount of the note, the remainder is the balance due on the note.

88. A note dated January 1st, 1846, was given for $1000, payable on demand, with interest at 6 per cent., on which were the following endorsements:

March 1st, 1846, received $75.00. July 15th, 1846, received $125.75. September 25th, 1846, received $250.00. Nov. 10th, 1846, received $300.00. What was the balance due on this note, January 1st, 1847? Ans. $295.474.

89. A, by his note dated July 1st, 1846, promised to pay B $625.50 in six months from date, with interest after three months. On this note were the following endorsements:

October 16th, 1846, received $250.75. November 25th, 1846, received $125.50. December 15th, 1846, received $75.25.

What was the balance due on this note January 1st, 1847, interest being allowed at 6 per cent.? Ans. $179. 294+. 90. A note dated July 1st, 1846, was given for $750, payable in six months, with interest from the date at 6 per cent. a year. On this note were the following endorsements: August 1st, 1846, received $75.75. September 16th, 1846, received $150.50. November 1st, 1846, received $250.25. What was the balance due on this note January 1st, 1847?

91. C, by his note dated April 1st, 1846, promised to pay D $1750 on demand, with interest at 6 per cent. a year. On this note were the following endorsements:

July 1st, 1846, received $125. October 1st, 1846, received $150. January 1st, 1847, received $500. What was the balance due on this note April 1st, 1847?

COMPOUND INTEREST.

Art. 150. COMPOUND INTEREST is that which is paid for the use of the principal, and also that which is paid for the use of the interest, after it becomes due; and it is found by adding the interest to the principal at the time it becomes payable, whether yearly, half-yearly, or quarter-yearly, and then making this amount a new principal.

RULE. When the interest is payable yearly, find the interest of the given principal for one year, add it to the principal, the amount is the principal for the next year. Find the amount of this principal, and of each succeeding principal, in the same manner, for the given number of years.

When the interest is payable half-yearly, or quarter-yearly, find the interest for a half-year, or a quarter-year, add the interest to the principal, the amount is the principal for the next half-year, or quarter-year. Find the amount of this principal and of each succeeding principal, in the same manner, for the given number of half-years or quarter-years.

Finally, subtract the given principal from the last amount; the remainder will be the compound interest.

1. What is the compound interest of $500 for 4 years, at 6 per cent., payable yearly?

$500 X .06=

$530 X.06=

$561.80 X.06:

OPERATION.

=

$500 given principal.

$30 interest for one year.

$530 amount, principal for the second year.
$31.80 interest for the second year.

$561.80 amount, principal for the third year.
$33.708 interest for the third year.

$595.508 amount, principal for the fourth year.

$595.508.06= $35.73048 interest for the fourth year.

$631.23848 amount for the fourth year.
$500.00 given principal deducted.

$131.23848 compound interest for four years.

2. What will be the compound interest of $1200 for 2 years, at 6 per cent., payable half-yearly? Ans. $150.61+. 3. What will be the compound interest of $675 for 2 years, at 6 per cent., interest payable quarter-yearly?

4. What will be the compound interest of $1500 for 5 years, at 6 per cent., payable yearly?