2. To calculate interest for months and days, at 6 per cent, RULE. Divide the principal by 2, placing the separatrix as in division of Federal money ; the quotient will be the interest for 1 month, in cents, &c. Multiply the interest for one month by the given number of months and decimal parts of a month, or for the days take even parts of a month. EXAMPLES. 1. What is the interest of $135,28 for 7 months and 15 days, or 7 months ? 2)135,28 or thus 2)135,28 Interest for 1 mo. 67,64 67,64 73 7, 5 33820 47348 507,300c. = $5 =5dols. 70. 3 mills. [07c. 3m, 2. What is the interest of $133,24 for 2 years in months ard 10 days, or 31į months, at 6 per cent per annum ? Ans. $20 87c. 4 zom, 3. Required the interest of $428 for 20 days, or of a month, at 6 per cent. Ans. $1 42c. 6m. + 4. What is the interest of $256,18 for 1 year 5 months and 15 days, or 17 months, at 6 per cent ? Ans. $22 41 51om. Note. As there are many short methods for casting interest at 6 per cent, it may sometimes be convenient, when the rate is any other than 6 per cent, to cast the interest first at 6 per cent, and add thereto, or subtract, such part as the rate is more or less than 6 per cent. Hence, to calculate interest at 7 per cent, we have the following concise and practịca! RULL FOR THE STATE OF NEW YORK. Add to the interest at 6 per cent, part of itself, the sum will be the interest at 7 per cent. EXAMPLES 1. What is the interest of 2. What is the interest of $148 for 1 year 5 months, or $125,40 for 1 year and 8 17 months, at 7 per cent ? months, at 7 per cent? Principal $148 125,40 Half the months= X 8} 10=} the mos. 11,84 add ()12,5400 int. at 6 pr.cț. 74 2,09 Int. at 6 per cent á 12,58 Ans. $14,63 2,09,6 Int. at 7 per cent. 14,67,6 +=14 dols. 67c. 6m. + 3. Required the interest of 4. Required the interest of $148 for 3 years and 4mos. $95,44 for 10 days, or of ą at 7 per cent per annum. month, at 7 per cent. $ cts. Princ. $148 2)95,44 20 } the months. 3)47,72 int. for 1 mo. [at 6 per cent: add 329,60 int. at 6 per ct. add ||15,90 do. for įmo. 4,93,3 2,65 Ans. $34,53,3=$34,53c. 3+ 18,55=18c. 51 m. COMMISSION, BROKERAGE, INSURANCE, &c. 1. Commission is an allowance of so much per cent to a correspondent or factor abroad, for buying and selling goods for his employer. 2. Brokerage is an allowance of so much per cent to persons assisting merchants and traders, in buying or selling goods. 3. Insurance is a premium at so much per cent, allowed to persons and offices for making good the loss of vessels, houses, merchandize, &c., which may happen from storms, fire, &c. The instrument which binds the parties is called a Policy. EXAMPLES. 1. What must I demand for selling goods to the amount of 548 dollars, at 21 per cent commission ? Ans. $12,33. 2. Required the commission on 875 dollars 56 cents, at 31 per cent ? Ans. $30 64c. 416 m. 3. What must my correspondent demand, who has sold goods to the amount of 3500 dollars 24 cents, at 3} per cent commission ? Ans. $135 63c. 41.m: 4. What is the brokerage upon 511 dollars 50 cents, at 33per cent ? Ans. $170,50 5. What may a broker demand who sells goods to the amount of $4500 at 127 per cent ? Ans. $562,50. 6. What is the insurance of $350, at 21 per cent ? Ans. $8,75. 7. A man's house, estimated at 2450 dollars, is insured against fire for 3} per cent per year; what insurance does he pay annually? Ans. $81 66c. 6m. + 8. What is the insurance of a ship and cargo, valued at $69450, at 15 per cent ? Ans. $107644. STOCK is the general name given to all monies invested in trading companies, or of any corporation or ford of Gov: ernment. When $100 of Stock sells for $100, it is said to be at par? when it sells for more, it is said to be above par ; and when it sells for less, it is said to be below par. 9. What is the value of $5421 of stock, at 1 12} per cent; that is, when $1 of stock sells for $1,121, which is 12} per cent above par, or 12} per cent advance? Ans. $6098 621. 10. What is the value of $950 bank stock at 95 per cent; that is 5 per cent below par ? Ans. $902 50. 11. What is the value of $1230 insurance stock, at 1187 per cerit, that is 184 per cent above par ? Ans. $1460 621. SIMPLE INTEREST BY DECIMALS. This is by many considered the best and most concise way of computing Interest. In this method of casting interest, (both simple and compound) the rate per cent is expressed in a decimal fraction, and when so expressed, is called the ratio. TABLE OF RATIOS. Rate per cent. Ratio. ,02 Ratio. Rate per cent. | Ratio. Rate per ccnt. 5 ,05 ,005 3 ,03 5) ,055 ,0075 4 ,04 6 ,06 ,01 41 ,045 7 ,07 2 Thus the interest of 1 dollar for one year, at 1 per cent, is 1 cent, or the oo part of 1 dollar; which expressed in a decimal fraction, is the ,01 of a dollar, or the ratio of one per cent; and of ,01 is 90025or the ratio of per cent. The of,01, is 005, or the ratio of } per cent; and of ,01, is ,0075, or the ratio of i per cent. So, likewise, the interest of $1 for one year, at 6 per cent, is 6 cents, or of one dollar, which written in a decimal fraction, is ,06, or the ratio of 6 per cent.; and so any other per cent expressed in a decimal fraction, is the ratio of that rate per cent as appears by the foregoing Table ; from which to find the interest of any sum of money for any given rate and time, we have the following 6 100 RULE. Multiply the principal, ratio, and time, continually together, (observing to place the decimal point the same as in multiplication of decimals) and the last product will be the interest required. EXAMPLES. 1. Required the interest of $315 36 for 4 years, at 6 per cent per annum. $315 36 principal. ,06 ratio. X 4 by time. 75,6864 Ans. $75 68cts. 618m. 2. What is the interest of $537 48 for 31 years, at 51 per cent per annum. Ans. $103 46 410. 3. What is the amount of $736 58 for 8 years, at 6 per cent per annum. Ans. $386 70 46 CASE II. The amount, time, and ratio, given to find the principal. RULE. Multiply the ratio and time together, and add 1 to the product for a divisor, by which divide the amount, and the quotient will be the principal required. EXAMPLES. 1. What principal will amount to $1138;2150 in 5 years, at 6 per cent per annum? ,06 X5+1=1,30)1138,2150($875,55 Ans. 2. What principal will amount to $2844,82650 in 71 years, at 7 per cent per annum. Ans. $1865,46. 3. What principal, at 6 per cent per annum, will amount to $2216,10, in 12 years. Ans. $1245. CASE II. The amount, principal, and time, given, to find the ratio. RULE. Subtract the principal from the amount, and divide the remainder by the product of the time and principal, and the quotient will be the ratio required. EXAMPLES: 1. At what rate per cent will $850,22 amount to 31156,2992 in 6 years? Ans. 6 per cent. From the amount $1156,2992 Subtract the principal 850,22 $850,22 X 6=5101,32)306,0792(,06=6 per cent. Aits. 306,0792 o 2. At what rate per cent will $325,00 amount to $390,00 in 4 years? Ans. ,05, or 5 per cent. 3. At what rate per cent will $450, amount to $698,625 in 83 years? Ans. ;065, or 64 per cent. 4. At what rate per cent will $381 gain $240,03 interest in 9 years. |