6. Find the interest of $72.85 for 3 years 5 mo. 27 d. For business purpose it is sufficiently exact to carry the work to mills or to tenths of mills at furthest, as in the shorter process. regarded. Answers are given as found by the shorter process. 7. How much must be paid for the use of $125.25 for 117 days at 6% per annum? What will be the amount? 8. Find the interest of $9280 for 1 yr. 7 mo. 7 days. 9. What is the interest of $13985 for 2 years 23 days? 10. What is the interest of $18.56 for 1 year 8 mo. 16 days? 11. What is the interest of $198 for 2 years 11 mo.? If it be required to find only the amount of a given sum at interest for a given time, the process may be made somewhat shorter than in the preceding example by adding the principal with the several items of interest, as follows: 12. Find the amount of $328 for 2 yr. 11 mo. 26 d. Principal, $328; Int. for 2 mo., $3.28; Int. 6 d., .328. Interest at other Rates than 6%. From the interest of any given sum at 6% the interest at any other rate can be readily found. Example. What is the interest of $329.75 for 1 yr. 5 mo. 23 d. at 6%? At 3%? 4%? 5%? 7% ? 8% ? 9% ? Interest at 6%. Solution. Prin., $329.75; Int. 2 mo. = $3.2975; Int. 6 d. = .32975. $26.3800 Int. 1 yr. 4 mo. (8 x 2 mo.) 1.64875 66 1 mo. (1/2 of 2 mo.) Shorter Process. $26.38 1.649 1.099 3 d. (1/2 of 6 d.) .165 Ans. $29.29280 Int. for 1 yr. 5 mo. 23 d. Ans. $29.293 Interest at other per cents. Having thus obtained the interest of $329.75 for 1 yr. 5 mo. 23 d. at 6%, the interest of the same sum for the same time— To find the time between the dates here given, follow the method of Ex. 1, page 231. 1872, Dec. 31, to 1879, Oct. 1. 11%, 1875, Dec. 25, to 1878, May 28. To find the interest of $1 for any given time at 6% affords an excellent mental exercise. 1. At 6% per annum, what is the interest of $1 for 3 yr. 5 mo. 7 d.? 205 mills, Solution. The interest of $1 at 6% for 41 mo. is 41 x 5 mills and for 7 d. it is 116 mills, hence for 3 yr. 5 mo. and 7 d. it is 206 16 mills. In like manner find the interest of $1 for From the interest of $1 for any given time the interest of any other sum may be readily obtained for the same time and at the same rate per cent. For some uses this method is preferable to any other. See Partial Payments. 308. To find the Rate; Principal, Interest, and Time being given. ORAL EXERCISES. 1. If 84 are paid for the use of $2 for 1 year, what is the rate per cent.? Analysis. At 1% per annum $2 (2004) would earn 24, but since the given interest (84) is 4 times 24, the rate must be 4 times 1% or 4%. 2. Thirty-six cents are paid for the use of $3 for 2 years. What is the rate per cent. charged? Analysis.-At 1% per annum the interest of $3 (3004) for 1 year would be 34, and for 2 years it would be 64, but since the interest paid (364) is 6 times 64, the rate must be 6 times 1% or 6%. 3. Find the rate per cent. if the annual interest on $840 is $42; if on $850 the interest is $34; if on $725 the interest is $432; if on $75 the interest is $3. *Note. The "time" given in this column being a multiple or aliquot of the corresponding "time" in the first column, the rate for the second column may be readily found from that of the first. But it must not be forgotten that, if the time is twice as long, the rate must be only 1/2 as great to produce the same interest, etc. |