12. In what time will $400 at 6% amount to $460 ? 13. In what time will $540 at 5% amount to $621 ? 14. In what time will any principal double itself at 5% ? 10%? 20%? 40%? 25%? 50%? 15. In what time will any principal treble itself at 5%? 10%? 20%? 25%? 40%? 163%? 16. In what time will a principal quadruple itself at 5%? 10%? 15%? 20%? 25%? 12% ? 17. The amount of a certain principal for a certain time at 5% is $600, and for the same time at 8%, $660; what are the principal and the time? 18. If I invest my money in bank stock yielding a dividend of 10 per cent., it will in a certain time amount to $9000; but if I loan it at 6% for the same time, it will amount to only $7800; what is the amount of money, and what the time? 3. TO FIND THE PRINCIPAL. 1. What principal will in 6 yr. 6 mo. at 4% give $52 interest? SOLUTION 1.-6 yr. 6 mo. equals 6 years. The interest on $1 for 61 yr. at 4% is 26 cents; hence $52 is the interest on as many dollars for the given time as 26 cents is contained times in $52, or $200. SOLUTION 2.-For 6 yr. 6 mo., or 61 yr., at 4%, 13 of the principal equals the interest. Since $52 is of the principal, of the principal is of $52, or $4, and 3%, or the principal, is 50 times $4, or $200. 2. What principal will in 5 yr. at 4% yield $20 interest? $60? $200? $1200? 3. What principal will in 6 yr. at 5% yield $60 interest? $150? $600? $9? 4. What principal will in 8 yr. at 4% yield $80 interest? $160? $640? $200 ? 5. What principal will in 6 yr. 8 mo. at 6% yield $100 interest? $120? $640? $1200? 6. A man pays annually on borrowed money $450, at 5%; how much has he borrowed? 7. How much money has a man on interest at 5%, if his annual income is $1030? 1 8. A gentleman sold his farm, to be paid for at the end of yr. 4 mo., interest at 6%. When payment was made the amount was $12,960; what was the price of the farm? 9. How much money must be put on interest to amount to $690 in 3 years at 5% ? 10. What principal will in 1 yr. 6 mo. at 8% amount to $224? 11. A debt which has been drawing interest for 6 yr. 4 mo. at 6% amounts to $552; what is the debt? 12. Mr. Williams invested of his money in the lumber trade, and at the end of 2 yr. 6 mo. sold his share for $10,800, at a profit of 8 per cent. yearly gain; how much money had he at first? PRESENT WORTH. The Present Worth of a debt is a sum which, if placed on interest at the legal rate for the given time, will amount to the face of the debt when it comes due. 1. What is the present worth of $440, due 2 yr. hence, at 5%? SOLUTION. Since the amount of $1 for 2 yr. at 5% is $1.10, the present worth of $440 is as many dollars as $1.10 is contained times in $440, or $400. 2. What is the present worth of $420, due 4 yr. hence, at 10%? 3. What is the present worth of $26, due 5 yr. hence, at 6%? 4. What is the present worth of $600, due 4 years hence, at 5% ? 5. What is the present worth of $360, due 31 yr. hence, at 6% ? 6. What is the present worth of $530, due 18 months hence, at 4% ? 7. The amount due on a mortgage which has been on interest for 8 years at 5% is $4900; what is the face of the mortgage? 8. If I buy a bill of paper amounting to $203, payment to be made in 3 months, what amount of cash will pay the bill now, interest at 6% ? TRADE DISCOUNT. Manufacturers, and sometimes wholesale merchants, have a fixed price on their goods, known as their list price. From this they make discounts varying as the market varies. Such discount is known as the trade discount, and the amount paid, as the net price. Frequently several discounts are given; as, 10% off and 5% for cash; or 30% and 10% off. In all such cases the discounts are deducted separately from the remainder left after each preceding discount has been deducted. Thus, in goods sold at $40 with 10% off and 5% for cash, 10% of $40, or $4, is first deducted, and then 5% from the $36 remaining. 1. Find the net price of goods sold at $25, discount 20 and 10. SOLUTION.-20% of $25 is $5; $25-$5 equals $20; 10% of $20 is $2; $20-$2 = $18. 2. Sold a bill of goods for $60, discount 20% and 5% off for cash; what was the net price? 3. If I buy books at $10 a dozen, discount being 40 and 10, what is the net price? 4. The list price of goods is $1.50; what is the net price if the discount is 10 and 20? 5. Which is the better for the purchaser, a discount of 10 and 20, or a discount of 20 and 10? 6. The list price of shoes is $40 a dozen, and the discount is 25 and 10; what do they cost a pair? 7. The list price of goods on 3 months' time is $4, the discount is 10% and 5% for cash; what is the net price? 8. What is the net 40, 25, and 10? price of goods listed at $10, discount BANK DISCOUNT. Bank Discount is the allowance made to a bank for the payment of a note before it comes due. Bank discount is the interest on the face of the note for the time it has to run, including three days of grace. 1. What is the bank discount of $120 for 60 days at 6% ? SUG.—The time is 63 days; the interest of $120 for 63 days at 6% is $1.26. Find the bank discount of- 10. $720 for 90 da. at 6%. 11. $200 for 60 da. at 5%. 12. $500 for 90 da. at 6%. 13. $300 for 95 da. at 6%. 14. $800 for 60 da. at 5%. 15. $500 for 30 da. at 6%. 16. $150 for 45 da. at 6%. 17. $120.30 for 90 da. at 6%. PROPORTIONAL PARTS. 1. Two men hire a pasture for $60: the first pastures 4 cows and the second 6 cows; how much should each pay? SOLUTION. Since the first pastured 4 cows and the second 6, they together pastured 10 cows. If the pasturage of 10 cows cost $60, the pasturage of 1 cow cost of $60, or $6; hence the pasturage of 4 cows cost 4 times $6, or $24, and the pasturage of 6 cows, 6 times $6, or $36. 2. If two men hire a horse for $25, the first using it 10 days and the second 15 days, how much should each pay? 3. Three boys bought 60 apples, the first paying 3 cents, the second 4 cents, and the third 5 cents; how many apples should each receive? 4. The pasturage of 5 cows for 4 weeks and 10 sheep for 4 weeks cost $30; how much does the pasturage of each cost, if the pasturage of a cow cost 4 times as much as the pasturage of a sheep? 5. Smith and Martin undertake to do a piece of work for $100: Smith sends 5 men for 6 days, and Martin 4 men for 5 days; how much should each receive? 6. 3 men, A, B, and C, undertake to do a piece of work for $348: A with 3 assistants works 10 days; B with 5 assistants works 6 days; and C with 9 assistants works 4 days; how much should each receive? 7. A furnishes 10 men, and B 16 boys, to do a piece of work for $90; how much should each receive, if the work of a man is worth twice that of a boy? 8. Three men hire a pasture for $124. C puts in 4 horses; D 10 cows; and E 30 sheep; how much should each pay if a cow eats twice as much as a sheep, and a horse three times as much as a sheep? 9. A puts into a pasture 20 sheep for 5 weeks; B, 10 cows for 4 weeks; and C, 5 horses for 6 weeks; how much should |