I. Reduce the shillings and pence to the decimal of a pound, and annex the result to the pounds:

II. Find the interest as though the sum were United States Money, after which reduce the decimal part to shillings and pence.

Examples.

1. What is the interest of £67 19s. 6d., at 6 per cent., for 3 years 8 months 16 days?

2. What is the interest of £127 15s. 4d., at 6 per cent., for 3 years and 3 months?

3. What is the interest of £107 16s. 10d., at 7 per cent., for 3 years, 6 months, and 6 days?

4. What will £279 13s. 8d. amount to, in 3 years and a half, at 5 per cent. per annum ?

PARTIAL PAYMENTS.

296. A PARTIAL PAYMENT is a payment of a part of the amount due on a note or bond.

We shall 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

295. How do you find the interest, when the principal is in pounds, shillings, and pence?

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 exceeds 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.

NOTE. In computing interest on notes, observe that the day on which a 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. Thus, a note dated on the first day of May, and falling due on the 16th of June, will bear interest but one month and 15 days.

$349.998.

Examples.

BUFFALO, 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.

On this note were indorsed the following payments:

Dec. 25th, 1826, received

July 10th, 1827,

Sept. 1st, 1828,

June 14th, 1829,

JAMES PAYWELL.

$49.998

4.998

15.008

99.999

What was due, April 15th, 1830?

296. What is a Partial Payment? What is the rule for computing interest, when there are partial payments?

Mary 20

PARTIAL PAYMENTS.

Principal on interest, from May 1st, 1826,

1819

243

$349.998

Interest to Dec. 25th, 1826, time of first payment,

7 months 24 days,

Payment, Dec. 25th, exceeding interest then due,

Remainder for a new principal,

49.998

$313.649

Interest of $313.649, from Dec. 25th, 1826, to June 14th, 1829, 2 years 5 months 19 days,

46.4721

Remainder for a new principal, June 14th, 1829,
Interest of $240.116, from June 14th, 1829, to
April 15th, 1830, 10 months 1 day,

$3469.32

Total due, April 15th, 1830,

120.005

$240.1161

12.0458

NEW YORK, Feb. 6th, 1825.

2. For value received, I promise to pay William Jenks, or order, three thousand four hundred and sixty-nine dollars and thirty-two cents, with interest from date, at 6 per cent.?

BILL SPENDTHRIFT.

On this note were indorsed the following payments:

May 16th, 1828, received $545.76.

What remained due, Aug. 11th, 1832?

3. A's note, of $635.84, was dated Sept. 5th, 1817; on which were indorsed the following payments, viz.: Nov. 13th, 1819, $416.08; May 10th, 1820, $152.00: what was due March 1st, 1821, the interest being 6 per cent.?

PROBLEMS IN INTEREST.

297. In all questions of Interest, there are four things considered, viz. :

1st, The Principal; 2d, The Rate of Interest; 3d, The Time; and 4th, The Amount of Interest.

If three of these are known, the fourth can be found. By Art. 292, the interest is found by multiplying together the principal, rate, and time in years; therefore, the interest is the product of the principal, rate, and time. Either of these factors is found by dividing the product by the product of the other two: Hence, we have the following principles:

1st, The principal is equal to interest divided by the rate and time: 2d, The rate is equal to interest divided by the principal and time: 3d, The time is equal to interest, divided by principal and rate.

Examples.

1. The interest of a certain sum for 4 years, at 7 per cent., is $266 what is the principal?

ANALYSIS.-The interest, $266, divided by the product of the rate and time, .07 × 4 = .28, will give the principal.

OPERATION.

.07 x 4.28. 266.28 $950= principal.

=

2. The interest of $3675, for 3 years, is $771.75: what is the rate?

3. The principal is $459, the interest $183.60, and the rate 8 per cent.: what is the time?

4. The interest of a certain sum for 3 years, at 6 per cent., is $40.50 what is the principal ?

5. The principal is $918, the interest $269.28, and the rate 4 per cent.: what is the time?

297. How many things are considered in every question of interest? What are they? The interest is the product of what factors? How may one of these factors be found? What are the three principles ?

6. What sum of money must be placed on interest at 7 per cent., for 3 yrs. 9 mos., that the interest may be $396?

7. In what time, at 7 per cent., will a mortgage of $8762.50, whose interest is unpaid, amount to $10000?

8. If, by purchasing a house for $5620, I have received, in 2 yrs. 3 mos. 15 days, $1800 rent: what rate of interest have I received?

9. A merchant, who had bought goods for $15960, sold them, at the end of 5 months 16 days, at an advance of 27 per cent.: what rate of interest did he receive?

10. What sum of money, at 6 per cent., will produce, in 2 yrs. 9 mos. 10 days, the same interest that $350 produces, at 8 per cent., in 3 yrs. 10 mos. 5 days?

11. In what time will $5000, at 7 per cent., produce the same interest that $9625 produces, at 6 per cent., in 4 yrs. 5 mos. 18 days?

COMPOUND INTEREST.

298. COMPOUND INTEREST is the interest of the amount of the principal and its unpaid interest.

This interest may be computed annually, semi-annually, quarterly, monthly, or daily. In Savings Banks, the interest is generally computed semi-annually.

From the definition, we deduce the following

Rule.-Compute the interest to the time at which it becomes due; then add it to the principal, and compute the interest on the amount as on a new principal: add the interest again to the principal, and compute the interest as before; do the same for all the times at which payments of interest become due; from the last result subtract the principal, and the remainder will be the compound interest.

298. What of Compound Interest? How do you compute it?