On this note were indorsed the following payments: Aug. 10, 1856, $156; Feb. 12, 1857, $200; June 1, 1858, $185. What was due Jan. 1, 1859? Ans. $105.50+.

317. In New Hampshire interest is allowed on the annual interest if not paid when due, in the nature of damages for its detention; and if payments are made before one year's interest has occurred, interest must be allowed or such payments for the balance of the year.

NEW HAMPSHIRE RULE.

I. Find the amonnt of the principal for one year, and deduct from it the amount of each payment of that year, from the time it was made up to the end of the year; the remainder will be a new principal, with which proceed as before.

II. If the settlement occur less than a year from the last annual term of interest, make the last term of interest a part of a year, accordingly.

$575.

KEENE, N. H., Aug. 4, 1858. 1. For value received, I promise to pay George Cooper, or order, five hundred seventy-five dollars, on demand, with interest annually. DAVID GREENMAN.

1860 ?

On this note were indorsed the following payments: Nov. 4, 1858, $64; Dec. 13, 1859, $48; March 16, 1860, $248 ; Sept. 28, 1860, $60. What was due on the note Nov. 4, Ans. $215.33. 318. When no payment whatever is made, upon a note promising annual interest, till the day of settlement, in New Hampshire the following is the

COURT RULE.

Compute separately the interest on the principal from the time the note is given to the time of settlement, and the interest on each year's interest from the time it should be paid to the time of settlement. The sum of the interests thus obtained, added to the principal, will be the sum due.

The New Hampshire rule. The New Hampshire court rule.

$500.

KEENE, N. H., Feb. 2, 1855. 1. Three years after date, I promise to pay James Clark, or order, five hundred dollars, for value received, with in terest annually till paid. JOHN S. BRIGGS. What is due on the above note, Aug. 2, 1859? Ans. $649.40.

PROBLEMS IN INTEREST.

319. In examples of interest there are five parts involved, the Principal, the Rate, the Time, the Interest, and the Amount.

CASE I.

320. The time, rate per cent., and interest being given, to find the principal.

1. What principal in 2 years, at 6 per cent., will gain $31.80 interest?

OPERATION.

$.12, interest of $1 in 2 year, at 6%.

$31.80.12 = $265, Ans.

ANALYSIS. Since $1, in 2 years, at 6 per cent., will gain $.12 interest, the principal that will gain $31.80,

at the same rate and time, must be as many dollars as $.12 is contained times in $31.80; dividing, we obtain $265, the required principal.

RULE. Divide the given interest by the interest of $1 for the given time and rate, and the quotient will be the principal.

EXAMPLES FOR PRACTICE.

2. What principal, at 6 per cent., will gain $28.121 in 6 years 3 months? Ans. $75. 3. What sum, put at interest for 4 months 18 days, at 4 per cent., will gain $9.20? Ans. $600. 4. What sum of money, invested at 7 per cent., will pay me an annual income of $1260? Ans. $18000.

5. What sum must be invested in real estate, yielding 10 per cent. profit in rents, to produce an income of $3370? Ans. $33700.

How many parts are considered in examples in interest? What are they? What is Case I? Give analysis. Rule.

CASE II.

321. The time, rate per cent., and amount being given, to find the principal.

1. What principal in 2 years 6 months, at 7 per cent., will amount to $88.125?

OPERATION.

$1.175 Amt. of $1 in 2 years 6 months, at 7%. $88.125 1.175 = $75, Ans.

ANALYSIS. Since $1, in

2 years 6 months, at 7

per cent., will amount to $1.175, the principal that will amount to $88.125, at the same rate and time, must be as many dollars as $1.175 is contained times in $88.125; dividing, we obtain $75, the required principal.

RULE. Divide the given amount by the amount of $1 for the given time and rate, and the quotient will be the principal required.

EXAMPLES FOR PRACTICE.

2. What principal, at 6 per cent., will amount to $655.20 in 8 months? Ans. $630. 3. What principal, at 5 per cent., will amount to $106.855 in 5 years 5 months and 9 days?

4. What sum, put at interest, at 5 5 months, will amount to $1897.545 ?

5. What sum, 3 years 4 months?

Ans. $84.

per cent., for 8 years Ans. $1297.09+.

at 7 per cent., will amount to $221.075 in Ans. $179.25. 6. What is the interest of that sum, for 11 years 8 days, at 10 per cent., which will at the given rate and time amount to $857.54? Ans. $460.04.

CASE III.

322. The principal, time, and interest being given, to find the rate per cent.

1. I lent $450 for 3 years, and received for interest $67.50; what was the rate per cent.?

Give Case II. Analysis. Rule. Case III.

must be equal to the number of times $13.50 is contained in $67.50; dividing, we obtain 5, the required rate per cent.

RULE. Divide the given interest by the interest on the principal for the given time at 1 per cent., and the quotient will be the rate per cent required.

EXAMPLES FOR PRACTICE.

2. If I pay $45 interest for the use of $500 for 3 years, what is the rate per cent.?

Ans. 3. 3. The interest of $180 for 1 year 2 months 6 days is $12.78? what is the rate %?

Ans. 6.

4. A man invests $2000 in bank stock, and receives a semi-annual dividend of $75; what is the rate per cent.? 5. At what per cent. must $1000 be loaned for 3 years 3 months and 29 days, to gain $183.18? Ans. 51.

6. A man builds a block of stores at a cost of $21640, and receives for them an annual rent of $2596.80; what per cent. does he receive on the investment? Ans. 12.

CASE IV.

323. Principal, interest, and rate per cent. being given, to find the time.

1. In what time will $360 gain $86.40 interest, at 6%?

as many as $21.60 is contained times in $86.40; dividing, we obtain 4 years, the required time.

RULE. Divide the given interest by the interest on the principal for 1 year, and the quotient will be the time required in years and decimals.

The decimal part of the quotient, if any, may be reduced to months and days (by 215).

EXAMPLES FOR PRACTICE.

2. The interest of $325 at 6 per cent. is $58.50; what is the time? Ans. 3 years. 3. B loaned $1600 at 6 per cent. until it amounted to $2000; what was the time? Ans. 4 years 2 months. 4. How long must $204 be on interest at 7 per cent., to amount to $217.09 ? Ans. 11 months. 5. Engaging in business, I borrowed $750 of a friend at 6 per cent., and kept it until it amounted to $942; how long did I retain it ? Ans. 4 years 3 months 6 days.

6. How long will it take cent. simple interest?

$200 to double itself at 6 per Ans. 16 years 8 months.

7. In what time will $675 double itself at 5%?

The time in years in which any sum will double itself may be found by dividing 100 by the rate per cent.

COMPOUND INTEREST.

324. Compound Interest is interest on both principal and interest, when the interest is not paid when due.

The simple interest may be added to the principal annually, semi-annually, or quarterly, as the parties may agree; but the taking of compound interest is not legal.

6

1. What is the compound interest of $200, for 3 years, at cent.?

per

Rule. In what time will any sum double itself at interest? What is compound interest ?