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1. At what time may the balance on the following accounts be paid at one time, without loss to either

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Ans. In 55 days; that is, February 25th.

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Ans. Due in 34 days from October 1st; that is, November 4th.

What is the bank discount and also the true discount of the following notes ; viz.,

3. Principal $300, due in 3 months, 3 days grace in each case, at 6%?

Ans. Bank discount, $4.65; True discount, $4.58. 4. Principal $500, due in 2 months, 3 days grace in each case, at 6%?

Ans. Bank discount, $5.25; True discount, $5.20. 5. Principal $2500, due in 4 months, 3 days grace in each case, at 6% ?

Ans. Bank discount, $51.25; True discount, $50.22.

6. Principal $6000, due in 1 year 3 months, 3 days grace in each case, at 6% ?

Ans. Bank discount, $453.00; True discount, $421.20.

7. What is the present worth of a note for $2000, due in 20 months, true discount, at 6%, no grace?

Ans. $18181821 8. How large a note, due in 2 years 6 months, with interest at 6%, will cancel a debt of $3450, due at the same time without interest ?

Ans. $3000. 9. What principal at 6% interest, will cancel a debt of $6000, due in 3 years 4 months ?

Ans. $5000. 10. What would be the bank discount on the debt, at the same rate for the same time without grace?

Ans. $1200.

REM. 1.-In true discount, the debt is the sum of the principal and interest; thus, $106 due in 1 year at 6% ; the principal or present worth is $100, and $6 is the interest on this principal; thus, $100 X 160 $6, and 100 + 6 = $106 ; and the fraction by which the debt is to be multiplied has 100 for its numerator and 100 + the interest on $100 for the time and rate for its denominator.

REM. 2.-Bank discount has for its principal the face of the note given for the debt.

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11. What is the time of maturity of a note dated Jan. 10th, 1872, discounted in bank for 90 days ?

Ans. April 12th. 12. If the note were discounted for 3 months, what would be the date of its maturity? Ans. April 13th.

REM.- When the time that a note has to run is expressed in days, the note will fall due in the exact number of days and 3 days grace added ; but when the time is expressed in months, the note will be due three days later in the month in which it falls, than in that in which it is given ?

In Ex. 11, the year 1872 was leap year.

13. A note for $5000, due April 1st, 1872, has the following endorsements : April 1st, 1873, Received $500 on note; April 1st, 1874, Received $1000 ; Oct. 16th, 1875, Received $1000; April 16th, 1877, Received $1000; how much was due on Oct. 16th, 1878, interest at 6%?

Ans. $3028.12. 14. A note of $6000, due Jan. 1st, 1871, interest at 6%, is endorsed: July 1st, 1871, Received $100; Jan. 1st, 1872, Received $100 ; June 19th, 1872, Received $100; Dec. 15th, 1872, Received $100; May 20th, 1873, Received $150; Oct. 30th, 1873, Received $150; Jan. 21st, 1874, Received $200. What was due Jan. 1st, 1875 ? $6000 x 100 x 4 = $1440 Interest.

900 Payments. $540 Balance on Interest. 6000 Principal $6540 Due Jan. 1st, 1875.

COR.-As the payments in Ex. 14 never exceeded the interest; their sum can be deducted from the interest for the whole time. If at any time the sum of the payments exceeded the interest to that time, then the interest to that time must be computed and added to the principal, from which the sum of the payments must be subtracted, and the remainder taken as principal.

REM.—Special attention should be given to the principle of partial payments and the examples given, which will obviate the pecessity of many similar examples.

15. How much cash will pay a debt of $1005, of which $475 is to be paid in 10 months, and the remainder in 15 months, interest at 6%, true discount ?

Ans. $945.40. 16. Sold 200 bbl. pork, commission 43%, freight $100, and remitted $2776.25; what was the pork sold for per barrel ?

Ans. $15. 17. If I fall 10% from my retail price, which is 30% advance on the cost, what per cent will my profit be?

Ans. 17%. 18. Took a risk of $40000 at 1%; reinsured } of it in another company at 4%, and 1 of it at 3%; what did I gain by reinsuring?

Ans. $22. 19. Bought a farm for $18000, one-third cash and the balance in two equal annual installments, which were discounted in bank without grace at 6%; what amount of cash pays for the farm ?

Ans. $16920. 20. Sold a quantity of goods for $1800, which was 10% less than cost ; what would have been the gain per cent if I had sold them for $2400 ?

Ans. 20%

21. What is the cost of a draft for $3000, at 3% premium, payable in 60 days and 3 days grace, 6% interest allowed ?

Ans. $2991.

REM.—The interest and the premium must be computed separately on the face of the draft.

22. In a section of land (640 acres) 30% is in wheat, 25% pasture, one-fourth meadow, and the balance woodland; how much wood-land was there? Ans. 128 acres.

23. The population of a city in 1870 was 240,000, which was 20% more than in 1860; and in 1865 it was 5% more than in 1860; what was the population in 1865?

Ans. 210,000. 24. A cargo of damaged goods was sold for $20,000, which was 333% less than cost; what was the cost ?

Ans. $30,000. 25. A merchant sells goods for $26,400, which was at a profit of 20%; what did the goods cost?

Ans. $22,000. 26. What is the commission on $56,000 at 1%? At 2%? 3%? 4%? %? %? %?

Ans. $56 ; $112 ; $168 ; $224; $14; $28; $42. 27. What per cent is any number of itself? Of double itself? Of three times itself ? Of } itself? Of itself?

Ans. 100%; 50% ; 33%; 200%; 400%. 28. If one number is 10% of another number, what per cent is the latter of the former? Ans. 1000%

Thus, 10 is 10% of 100, and 10 is 100% of itself (10), and 100 is 1000% of 10.

29. A merchant made a profit of $200, which was 20% of his investment; what was the investment? 20% = $200; 100% = $1000.

Ans. $1000,

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