ANALYSIS.

ANALYTICAL STEPS.-1. Find the interest on the face of the note, to the time of the 1st payment.

2. Find the new principal, June 13, 1858.

3. Find the interest on this principal, to the time of the 2nd payment.

4. Find the new principal, Dec. 11, 1858.

5. Find the interest on this principal, to the time of the 3rd payment.

6. Find the new principal, Sept. 13, 1859.

7. Find the interest on the principal, to the time of the 4th payment.

8. Find the new principal, July 9, 1860.

9. Find the interest on this principal, to the time of the 5th payment.

10. Find the interest on this principal, to the time of the 6th payment.

11. Find the new principal, Dec. 29, 1862.

12. Find the interest on this principal, to Jan. 9, 1863. 13. Find the amount due, Jan. 9, 1863.

611. $4893.

LESSON LXXIII.

CINCINNATUS, N. Y., Oct. 9, 1860. Sixteen months from date, we promise to pay Oscar Osgood, or order, four hundred eighty-nine dollars thirty-nine cents, with interest from date, value received.*

RICHARD F. WESTON.
JOHN C. LEE.

INDORSEMENTS.

Nov. 3, 1860, $29.13.
Jan. 11, 1861, 125.

Mar. 11, 1861, $5.37.
May 13, 1861, 91.61.

What was the amount when the note became due?

*NOTE.-Notes on time do not draw interest until they are due, unless it is so stated in the body of the note. Demand notes draw interest from date of demand, and notes on time, after they become due, although there be nothing said in them about interest.

612. $984.

UNADILLA, N. Y., Aug. 8, 1860. Three years from date, we jointly and severally promise to pay Israel Putnam, or bearer, nine hundred eighty-four dollars, with interest after four months, value received.

How much is to be paid when the note becomes due?

613. $500.

BROOKLYN, Sept. 9, 1859. One year from date, I promise to pay O. H. Hall, five hundred dollars, value received.*

Received on the within note:

Jan. 12, 1861, $300.50.
June 13, 1861, $21.63.

WILLIAM H. WILLIAMS.

Apr. 25, 1863, $2.23.

May 27, 1864, $25.50.

How much was due when the note was paid, Oct. 18, 1864?

614. $1345.10. 38

HARTFORD, Jan. 13, 1862.

Thirty days from date, I promise to pay Ayres Jennings & Co., one thousand three hundred forty-five dollars thirtyeight cents, at 8 per cent., value received.

What was due April 8, 1864?

THEODORE LYON.

QUESTIONS. Give the analysis of finding the value of stock, when at a premium. (204.) Write a rule from the analysis. Give the analysis of finding the quantity of stock that can be purchased for

*NOTE. This note is not negotiable, and it draws interest only after it becomes due.

Write a rule from the analysis. What is

a certain sum. (205.)

profit and loss? (206.)

LESSON LXXIV.

PROBLEMS IN INTEREST.

251. In Problems in Interest there are five parts to be considered: 1st. The Principal. 2d. The Rate per cent. 3d. The Time. 4th. The Interest. 5th. The Amount. These may be symbolized by the following abbreviations:

P. Principal.
R.=Rate per cent.

A. Amount.

T.=Time.

I. Interest.

=

These parts are so related to each other, that, any three of them being known, the other may be found.

252. Prob. I.—Given the principal, rate per cent., and time, to find the interest.

1

What is the interest of $57 for 3 years, at 7

MODEL OPERATION.

1. $57X.07=$3.99.

2. $3.99X3=$11.97.

per cent.?

ANALYSIS.-1. If the interest on $1 for one year is 7 hundredths of a dollar, on $57 it is 57 times 7 hundredths of a dollar, which are 399 hundredths dollars, or $3.99.

2. If the interest on $57 for one year is $3.99, for 3 years it is 3 times $3.99, which are $11.97.

Therefore, the interest on $57 for 3 years, at 7 per cent., is $11.97.

FORMULA: P.XR.XT.-I.

NOTE.-Require the pupil to write a rule from the formula.

615. What is the interest on $37.86 for 9 yrs. 3 mo. 11 da., at 8 per cent.?

616. What is the interest on $27.41, for 2 yrs. 3 mo. 27 da., at 7 per cent.?

QUESTIONS.-Give the analysis of finding the amount of gain, when the cost and gain per cent. are given. (207.) Write a rule from the analysis. Give the analysis of finding the gain or loss per cent., when the cost and selling price are given. (208.) Write a rule from the analysis. Give the analysis of finding the selling price, when the cost and gain or loss per cent. are given. (209.) Write a rule from the analysis.

LESSON LXXV.

253. Prob. II.-Given the time, rate per cent., and interest, to find the principal.

What principal in 2 yrs. 6 mo., at 6 per cent., will gain $25.36 interest?

MODEL OPERATION.

1. $1X.06×2=$0.15, int. on $1.

2. $25.36÷.15=$169.066.

ANALYSIS.-1. The interest on $1 for 2 yrs. 6 mo., at 6 per cent., is $0.15.

2. If it requires $1 to gain $0.15 in 2 yrs. 6 mo., at 6 per cent., to gain $25.36 will require as many dollars as $0.15 is contained times in $25.36, which are 169.066.

Therefore, $169.066 are required to gain $25.36 in 2 yrs. 6 mo., at 6 per cent.

FORMULA:

I.
$1×R.XT=P.

NOTE.-Require the pupil to write a rule from the formula.

617. A gentleman loaned money at 7 per cent., and received $700 interest a year; how much money did he loan? 618. What principal will, in 4 yrs. 8 mo. 24 da., at 6 per cent., give $18.88 interest?

619. What principal will, in 4 mo. 6 da., at 7 per cent., give $25.50 interest?

620. A gentleman bequeathes his wife $600 a year, and his son $400 a year; what sum must be invested, at 7. per cent. interest, to produce these amounts?

621. What principal will, in 1 yr. 11 mo. 26 da., at 5 per cent., produce $188.88?

622. A widow is receiving $1888 per annum; what is her property, supposing it invested at 7 per cent.?

623. What principal will, in 8 yrs., at 7 per cent., produce $4000 interest?

624. What principal will, in 3 yrs. 3 mo. 3 da., at 5 per cent., produce $28.75?

625. What principal will, in 6 yrs., at 7 per cent., produce $800.50 interest?

626. An estate was divided among three children: the first loans his money at 8 per cent. interest, and receives $400 a year; the second loans his at 7 per cent., and receives $450.42 interest per annum; the third loans his at 5 per cent., and receives $400.75 interest per annum; what was the value of the estate?

QUESTIONS.-Give the analysis of finding the cost when the selling price and gain or loss per cent. are given. (210.) Write a rule from the analysis. What is insurance? (211.) Who is the insurer? (212.) Who is the insured? (213.) What is the policy? (214.) What is the premium? (215.) Give the analysis of finding the amount of the premium, when the rate per cent. is given. (216.) Write a rule from the analysis.

LESSON LXXVI.

254. Prob. III.-Given the time, rate per cent., and amount, to find the principal.

What principal, in 3 years 4 months, at 8 per cent., will produce an amount of $73.86?