In small business this method will be sufficiently exact, but in large sums it is advisable to calculate by the preceeding rules, because 30 days fall short of of a year. How to find the time a Note or Bond has been on Interest.

Lesson 17.-Suppose a note was given on interest April 2, 1813, and paid March 4, 1816; how many years, months, and days does it draw interest?

Answer, 2 years, 11 months, and 2 days.

Operation.

March 4, 1816,

April 2, 1813,

Answer,

1816 years 2 m. 4 days.

Allow 30 days to be one month, and 12 month one

1. The Note was paid on the 4th of March, 1816, which time we call 1816, years on New-year's day last before the payment, and the 4th of March we say is 2 months and 4 days after New-year's day.

2. So again for the time of signing the note, we say that the 2nd of April was 3 months and 2 days after New-year's day 1813. Subtract and carry at 30 and at 12.

Application.-What is the interest of a Note of $450.75 for 2 years 11 mo. and 2 days at 7 per cent. per annum? Answer, $92.20+ Directions.-First, find the interest for 3 years; - then take one twelfth of one year's interest from that

sum, the difference will be 2 years 11 mo. interest. Secondly, take the 15th part of one month's interest

for 2 days.

9465.75 three years interest.

262.93 one month's interest subtracted.

9202.182 two year's and 11 month's interest, 17. 528 two day's interest or 15th of one mo,

9220.1348 Ans. $92.20 cents, and .348 thousandths of a cent.+

Lesson 18.-If a Note were given on interest, 5th May, 1812, and paid March 2, 1817, what time should be allowed for interest?

Answer, 4 years, 9 mo. 27 days.

Operation.

9

27

Application.-What is the amount of $16.50, for 4 years, 9 months and 27 days, at 7 per cent. per annum? Answer, $22.07+ Observations.-1. In this case obtain the interest for 4 years; then take half the interest for 1 year, and the half of that half for 9 months.

2. For 27 days divide the interest of 1 year by 12, the quotient will be the interest of 1 month, viz. 9.6250 cents; subtract one-tenth of a month's interest,

that is 3 days, from that sum, the remainder will be 27 day's interest, viz. 8.6625 cents.

557 2875 int. for 4 yrs. 9 mo. 27 days. principal.

1650

2207 2875 amount, or answer.

COMPOUND INTEREST.

Find the interest of the given sum for 1 year, add that interest to the principal and call it the amount. Take this amount for the principal of the second year Find the amount for the second year and make it the principal of the third year, &c. &c.

NOTE. Subtract the given sum from the last amount, the remainder will be compound interest.

• DECIMAL INTEREST.

Make a common multiplier for the rate per cent. thus: If 100 cents in one year give 7 cents interest, what will 1 cent give in the same time?

Principal,

100: 7 :: 1
1

cent.

100)7.00

.07

Here appears to be 7 hundredths o. a cent for the interest of 1 cent 1 year: This .07 we will call a common multiplier, by which any number of cents may be multiplied, and the product will be their interest at 7 per cent. for 1 year.

For 6 per cent. .06 will be a common multiplier. For 5 per cent. .05; for 5, .055, &c. They are all found by the rule of proportion as before.

Lesson 18.-What is the interest of 354 cents for 1 year at 7 per cent.? Ans. 24.78 cents.

Principal,

354 cents.

Common multiplier, .07

24.78

Lesson 19.-What is the interest of 13 dollars 371

cents for 1 year, at 6 per cent. ?

Ans. 60.25 cts.

1337.5 cts.

.06

60.250 cts.

In the last lesson we point off three decimals in the product, because there are three in the factors, that is, one in the multiplicand, and two in the multiplier. LESSON 20.

What is the interest of 316 dollars and 50 cents for 4 years at 33 per cent per annum? Ans. 44 dol. 31 cents. Principal, 31650 cts. Com. multiplier, .035

LESSON 21. My agent has bought cattle to the amount of 3452 dollars S7 cts.; how much will his commission be at the rate of two and a half per cent.? Ans. S6 dol. 32 cents. Principal, Com. mult.

345287.5 cts.

158250

.025

Answer,

Lesson 22.-What is the interest of £32 Is. 6d. for 5 years at 6 per cent. per annum? £10 8s. 5d. 3q. 4 tenths.

A common multiplier is found in this case by the same proportion as that above Lesson 18, viz.

If 100 pounds in a year will give 6.5 pounds interest, what will one pound give in the same time? Answer, .065 of a pound.*

COMPOUND INTEREST CALCULATED BY LOGARITHMS.

Pule.-Add the rate per cent. to 100; find the Logarithm of that sum, and subtract from it the Logarithm of 100; call the difference Logratio; multiply the Logratio by the number of years, and to that product add the Logarithm of the principal; the natural number of the last Logarithm will be the amount in Compound Interest.

Example 1.-What is the amount of $500 for 3 years, at 7 per cent. per annum, compound interest? Answer, $612.50.

Operation.

Rate per cent. 7+100-107. Log. of 107 is 2.02938

Logarithm of 100 is

Principal 500. The Logarithm of which is 2.69897

Logarithm of the amount,

2.78711

The natural number to 2.78711 is 612.5, the amount required.

* This common multiplier can bo on a memorandum, or retailed in memory.