New England States the legal rate is 6 per cent., while in the State of New York it is 7 per cent. The sum of money borrowed, or upon which the interest is computed, is called the principal. The principal, with the interest added to it, is called the amount. What is Interest? How is it estimated? What is the rate per cent. when $6 is paid for the use of $100 for one year? What is the rate per cent. when $5 is in the same way paid? Is the rate per cent. generally fixed by law? What is the legal rate per cent. in the New England States? What is it in the State of New York? What is the principal? What is the amount? CASE L To find the interest on any given principal, for any whole number of years, at any given rate per cent. Suppose we wish the interest of $365-50 for 3 years, at 7 per cent. ART. 112, we Performing the $25.585 for one By the definition of interest money, it follows that the interest of $365-50 for one year, at 7 per cent., is 7 per cent. of $365-50; which by rule under obtain, by multiplying $365-50 by 0-07. multiplication, we have $365-50×0.07 year's interest, which, multiplied by 3, the number of years, will give us $76-755 for the interest of $365.50 for 3 years at 7 per cent. Hence the following RULE. Multiply the principal by the rate per cent., expressed in decimals, and that product by the number of years; observing the usual rule for pointing off the decimal figures. EXAMPLES. What is the interest of $573.15 for 5 years at 6 per Ans. $120. 2. What is the interest of $600 for 4 years at 5 pc cent.? 3. What is the interest of $725 for 8 years at 4 per cent.? Ans. $261. 4. What is the interest of $149 for 5 years at 2 per cent.? Ans. $14.90. 5. What is the interest of $225.25 for 10 years at 4 per cent. ? Ans. $90.10. 6. What is the interest of $311.30 for 11 years at 10 per cent. ? Ans. $342-43. 7. What is the interest of $501.50 for 2 years at 3 per cent. ? Ans. $35.105. CASE II. To find the interest on any given principal, for any given time, at any given rate per cent. Suppose we wish the interest of $126 for 3 years 5 months and 15 days, at 7 per cent. 66 of 1 mo. 3675-15 days' Ans. $30-5025-3 yrs. 5 mos. and 15 days' int Hence the following RULE. Multiply the principal by the rate per cent. expressed in decimals; the product will give one year's interest, which, multiplied by the number of years, will give the interest for the tine expressed in years. Then find the interest for the months and days by means of aliquot parts, as in Practice. EXAMPLES. 1. What is the interest of $39-42 for 1 year, 5 months, and 11 days, at 7 per cent.? NOTE. We have not extended our work to more than three places of decimals, but have added 1 to the third place whenever the fourth decimal figure would be 5 or greater. 2. What is the interest of $47.13 for 7 months and 21 days, at 7 per cent.? Ans. 2.118. 3. What is the interest of $321.21 for 3 months and 15 days, at 6 per cent. ? Ans. $5.621. 4. What is the interest of $270 for 2 months and 8 days, at 7 per cent. ? Ans. $3.57. 5. What is the interest of $404-44 for year, 5 months and 4 days, at 7 per cent.? Ans. $40-422. 6. What is the interest of $99.99 for 11 months and 29 days, at 5 per cent. ? Ans. $4.986. 7. What is the interest of $37.50 for 6 months and 10 days, at 6 per cent. ? Ans. $1.287. 8. What is the interest of $49.49 for 8 months and 8 days, at 7 per Ans. $2.386. cent. ? CASE III. To find the interest on any given principal for any given time at 6 per cent.? The interest on $100 for one year, at 6 per cent., being $6, it follows that the interest on $1, for one year, is $0.06; and since 2 months is of a year, the interest on $1, for two months, is $0.01; again, since 6 days is of 2 months, when we reckon 30 days to each month, it follows that the interest on $1, for 6 days, is $0.001. Hence, if we call half the number of months, CENTS, and one-sixth the number of days, MILLS, we shall obtain the interest of $1 for the given time, at 6 per cent. T The interest of $1 being multiplied by the number of dollars in the given principal, will obviously give the in terest sought. As an example, suppose we wish the interest of $125 for 1 year, 5 months and 18 days, at 6 per cent. $0.085=int. of $1 for 1 y. 5 m. 17 months. $0-088=int. of $1 for 1 y. 5 m. and 18 days. If row we multiply 80-088 by 125, the number of dollars in the principal; or, which is the same thing, if we multiply $125 by 0-088, we shall find $125 ×0·088=$1: ̧ for the interest sought. Hence we have this RULE. 1. Call half the number of months, CENTS; one-sixth the number of days, MILLS; and the result will be the interest of $1 for the given time. II. Multiply the interest of $1, thus found, by the number of dollars in the given principal, and the product being pointed off by the rule for decimals, will give the interest required. EXAMPLES. 1. What is the interest of $49.37, for 13 months and 15 days, at 6 per cent.? In this example, we find the interest on $1, for 13 months and 15 days, at 6 per cent., to be $0.0675, which, multiplied by 49-37, the number of dollars in the principal, gives $3.332475, for the interest on $49-37, for the given time. 2. What is the interest of $608-62, for 1 year and 9 months, at 6 per cent.? Ans. $63.9051. 3. What is the interest of $341.13, for 7 years and 9 days, at 6 per cent.? Ans. $143.786295. |