But the interest is required at 4 per cent. instead of at 6 per cent. If of 6 be taken from 6, the remainder will be 4; hence, if of $23.10, the interest at 6 per cent., be taken from $23 10, the remainder will be the interest at 4 per cent. Performing this operation, we have $23.10 - of $23·10=$17.325 for the interest of $300 for 1 year, 3 months and 12 days, at 4 per cent.

Hence, we have this

RULE.

Find the interest on the given principal, for the given time, at 6 per cent., by Case III. Then increase, or decrease, this interest by the same part of itself, as it would be necessary to increase, or decrease 6 per cent., in order to make it agree with the given rate per cent.

EXAMPLES.

1. What is the interest of $19.41, for 1 year, 7 months and 13 days, at 7 per cent.?

In this example, we find by Case III. that the interest of $19.41, for 1 year, 7 months and 13 days, at 6 per cent., is $1.886005. Since 6, increased by its sixth part, equals 7, it will be necessary to increase the interest just found for 6 per cent., by its sixth part, which becomes $2.2003394, for the interest at 7 per cent.

2. What is the interest of $530, for 3 years and 6 months, at 6 per cent. ? Ans. $92.75. In this example, it was necessary to decrease the interest of 6 per cent., by its sixth part.

3. What is the interest of $5.37, for 4 years and 12 days, at 8 per cent. ? Ans. $1.73272. In this example, we increase the interest at 6 per cent., by its third part.

4. What is the interest of $4070, for 3 months, at 9 per cent. ? Ans. $91.575.

5. What is the interest of $3671, for 6 months, at 10 per cent.? Ans. $183.55.

6. What is the interest of $4920-05, for 3 months, at 4 per cent.? Ans. $49.2005.

7. What is the interest of $40-17, for 3 months and 18 days, at 3 per cent.? Ans. $0.36153. 8. What is the interest of $37.13, for 5 months and 12 days, at 4 per cent.? Ans. $0.7518825. 9. What is the interest of $489, for 3 years and 4 months, at 5 per cent.?

Ans. $89.65. 10. What is the interest of $700, for 1 year and 9 months, at 7 per cent. ? Ans. $85.75.

NOTE. When the principal is given in English money, we must reduce the shillings, pence and farthings, to the decimal of a £; and then proceed as in Federal money.

11. What is the interest of £75 13s. 6d., for 3 years and 5 months, at 6 per cent.?

In this example, 13s. 6d., reduced to the decimal of a £, is 0.675, so that our principal is £75-675; the interest on £1, for 3 years and 5 months, at 6 per cent., is £0-205, which, multiplied by 75-675, gives £15.513375-£15 10s. 3d for the interest required. (See ART. 99.)

12. What is the interest of £14 5s. 34d., for 4 years 6 months and 14 days, at 7 per cent.?

Ans. £4 10s. 77%d. nearly. 13. What is the interest of £1 7s. 6d., for 2 years and 6 months, at 4 per cent.? Ans. £0 3s. 1d.

14. What is the interest of £105 10s. 6d., for 91 months, at 5 per cent. ? Ans. £4 3s. 6d. 1·95far.

INTEREST WHEN THE TIME IS ESTIMATED IN DAYS.

114. THUS far, we have considered the time, for which interest is to be computed, as estimated in months and days, counting a month as of a year, and 1 day as of a month, or of a year.

Now, as some months have 31 days, and others less than 31, we, by the previous methods, obtain sometimes too much interest, and sometimes too little, but the error must always be small.

We will, under this Article, explain the more accurate method by means of days, which is sometimes called the Commercial Method.

Suppose we wish the interest of $500 from May 15th to November 20th, at 7 per cent.

By CASE I., ART. 113, we find $500 × 0·07=$35 for one year's interest of $500, at 7 per cent. By Table under ART. 76, we find 189 days from May 15th to November 20th

It is obvious that the interest for 189 days must be the same fractional part of one year's interest, that 189 days is of 365 days. Hence, $35 x 18 8 = 435 x 182 $18·123+ for the interest of $500 from May 15th to November 20th, at 7 per cent.

Hence this

RULE.

Multiply the principal by the rate per cent. expressed in decimals; the product will be one year's interest; which multiply by the time expressed in days, and divide this last product by 365, and the quotient will be the interest sought.

EXAMPLES.

1. A note of $37.37 was given May 3, 1848; how much was due on it Dec. 27, 1848, at 7 per cent.?

By the table under ART. 76, we find 238 days from May 3 to Dec. 27.

365)622-5842(1.705 interest sought in dollars.

2. A note of $365 was given July 4, 1847; what will it amount to, June 1, 1849, interest being 7 per cent. ?

Ans.

3. What is the interest on $100 from January 13th to November 15, it being Leap-year, and interest being 6 per cent.? Ans. $5.047.

4. What is the interest on $216 from March 10th to December 1st, interest being 5 per cent.? Ans. $7.871. 5. What is the interest on $107 from April 12th to July 4th, interest being 7 per cent. ? Ans. $1.703.

6. What is the interest on $1000 from June 20th to August 13th, interest being 7 per cent.? Ans. $10·356. 7. What is the interest on $730 from July 4th to December 25th, interest being 6 per cent.? Ans. $20.88. 8. What is the interest on $63.37 from August 9th to December 31st, interest being 7 per cent.? Ans. $1.75.

PARTIAL PAYMENTS.

115. WHEN notes, bonds, or obligations receive partial payments, or indorsements,* the rule adopted by the Supreme Court of the United States is as follows:

RULE.

"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. If the payment exceed 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."

The above rule has been adopted by New York, Massa

*From a Latin phrase, in dorso, meaning "upon the back;" because the pay sents are written across the back of the note.