On this note were the following Endorsements. April 1, 1830, received $40 $8 How much remains due August 16, 1831, interest at 6 per cent ? Ans. $455,57. COMPOUND INTEREST Is that which arises both from the principal and interest ; that is, when the interest is added to the principal at the end of the year, and on that amount the interest cast for another year and added as before; and so on for any number of years. RULE. Find the interest for 1 year, and add it to the principal; call this the amount for the first year. Find the interest of this amount and add it thereto for the amount of the second. and so on for any number of years. Subtract the original principal from the last amount, and the remainder will be the Compound Interest. EXAMPLES. 1. What is the amount, and what the compound interest, of $150 for 3 years, at 6 per cent per annum? 159,00 amount for the 1st year, or 2d principal. 6 9,5400 interest. 159, =2d principal added. 168,5400=amount for the 2d year, or 3d principal. 6 10,112400-interest. [Carried over.) [Operation brought up.] 10,112400 interest. 168,54 = $178,652400 amount for 3 years=$178 65cts. 2,4m. first principal subtracted. 150, $28,652400 compound int. for 3yrs.-$28 65c. 2,4m. 2. What will $125 amount to in 4 years, at 6 per cent per annum, compound interest? Ans. $157,80c. 9m+ 3. What is the compound interest of $750 for 5 years, at 5 per cent? Ans. $207,21+ 4. What will be the amount of $410,50 for 3 years, at 6 percent? Ans. $488,912+ 5. What is the compound interest of $500 for 3 years, at per cent? Ans. $95,50c. 8m. 6. What is the amount of $1000 for 4 years, at 6 per cent per annum, compound interest? 6 Ans. $1262, 47c. 6,9m.+ Note. When there are months, or months and days, in the question, first find the amount for the years, and on that amount calculate the interest for the months, or months and days; this interest added to the amount for the years will give the amount required. 7. What will $148,25 amount to in 3 years and 6 months, at 6 per cent? 8. What is the compound interest of months and 15 days, at 5 per cent? BY DECIMALS. RULE. Ans. $181,865+ $500 for 4 years 2 Ans. $114,08+ · Multiply the principal continually by the amount of $1 or £1 for one year, at the given rate per cent, until the number of multiplications is equal to the given number of years. Thus, at 5 per cent, the amount for 1 year is 1,05; at 6 per cent, it is 1,06, &c. 1. What will be the amount of $500 for 3 years, at 6 per cent per annum? Thus, 500 × 1,06 × 1,06 × 1,06=$595,508, Ans. Or, find the amount of $1, for 3 years, at 6 per cent per annum. 1,06 amount for 1 year. 1,06 636 106 Note. Since the amount of 2 dols. will be just twice as much as 1 dollar, and 3 dollars 3 times as much as 1 dollar, and so on, it is evident 1,1236 amount for 2 yrs. that if we multiply the amount 1,06 67416 11236 of $1 by any given number of dollars, we have the amount for that number of dollars. 1,191016 amount for 3 yrs. Thus, the amount of $1 for 3 years, at 6 per cent, is 1,191016; this, multiplied by $500, gives the amount $595,508, the same as in example 1st. Hence we may have a Table showing the amount of £1 or $1, for any number of years, by which we may easily find the amount of any snm for the same time, by multiplying the amount taken from the Table by the given sum. A TABLE, Showing the amount of $1, or £1, for any number of years, not exceeding 20, at 5 and 6 per cent, Compound Interest. YEARS. 15 PER CENT. 6 PER CENT. YEARS. 5 PER CENT. 6 PER CENT. 3. What is the amouut, and what the Compound Interest, of $350 for 5 years, at 6 per cent ? An't of $1 for 5yrs. at 6 per cent, by the Table 1,33822 Multiply by the principal, Answer. Amount for 5 years, Leaves the Compound Interest, 'X 350 6691100 401466 =468,37700 4. What is the amount, and what the Compound Interest of $311,25 for 6 years, at 5 per cent? $417,103 Amount. Ans. $105,85,3 Compound Interest. [The learner may work all the preceding examples in Compound Interest by the foregoing Table of Amounts, if necessary for further practice.] Note. Any sum at 6 per cent, Simple Interest will double itself in 16 years 8 months; and at Compound Interest, in 11 years 8 months and 22 days. Questions. What concise Rule have we for calcu lating interest for New York State? What is Commission?-Brokerage ?Insurance ?-Stock? When is Stock said to be at par?. When above par? When below par? When the rate per cent is expressed in a Decimal Fraction, what is it called? Havinng the amount time and rate per cent given, how do you find the principal' Having the amount, principal and time given, how do you find the rate per cent? Having the principal, rate per cent and amount given, how do you find the time? How do you compute the interest on Notes, or obligations where endorsements have been made? What is Compound Interest? What is the Rule for Compound Interest? DISCOUNT Is an allowance made for the payment of any sum of money before it becomes due. After the discount is deducted, the remainder is the present worth; or, such a sum as, if put at interest, at the given rate and time, would amount to the given sum. RULE. 1. As the amount of $100, or £100, at the given rate and time, is to the interest of 100, at the same rate and time, so is the given sum to the discount. Subtract the discount from the given sum, and the remainder is the present worth.—Or by 2 Divide the given sum by the amount of $1, or £1, at the given rate and time, the quotient will be the present worth. Subtract the present worth from the given sum, and the remainder is the discount." EXAMPLES. 1. What is the present worth of $132,50, due 1 year hence, at 6 per cent discount? 2. What sum, in ready money, will discharge a debt of £540, due 3 years 4 months hence, at 6 per cent? Am't of £1 for 3 years 4 months, at 6 per cent, 4 } £ £ £ 1,20)540,00(450 Ans. 3. What is the present worth of 500 dollars due 2 years months hence, at 5 per cent? $ $ cts. m. 1,125)500,000)444,44,4+Ans. 4. What is the present worth of $1080, due 5 years 10 months hence, at 6 per cent? Ans. $800. 5. What is the discount of $460, due 2 years 6 months hence, at 6 per cent ? Ans. $60. 6. Bought goods to the amount of $1260,50 on eight months credit: how much ready money must I pay to discharge the same, discounting at 6 per cent? Ans. $1212, 1c. 9m.+ Note. When sundry sums are payable at different times, find the present worth of each payment separately, and then add them together. *This is precisely the same as Case II, Simple Interest by Decimals, since the present worth of any sum is such a principal as, if put at interest for the given rate and time, would amount to said sum, it follows that we have the amount, time and rate per cent given, to find the principal, or present worth. |