172. Questions on the preceding Table. 1. How long must a principal be on interest that the inter 173. Applications of the foregoing Table. 1. What is the interest of $156.96 for each time mentioned in the table? Answer. The interest of $156.96 for 200 mo. = $156.96; for 100 = of $156.96; for 663 mo., or 5 yr. 6 mo. 20 da., = mo., or 8 yr. 4 mo., = of $156.96; &c. of of $1.57; / The interest of $156.96 for 20 mo. = $15.696; for 10 mo. = $15.696; for 6 mo., or 6 mo. 20 da., = of $15.696; &c. The interest of $156.96 for 2 mo. = $1.57; for 1 mo. = for 20 da. of $1.57; = &c. NOTE. The object in giving the answer in the above form is to direct the pupil's attention exclusively to the method of computing the interest; but as soon as he has had practice enough to enable him to tell at once what part of the principal, or of some convenient part of the principal, the interest for any of the above-mentioned times is, he should compute the interest in each case. Thus, the interest of $156.96 for 100 mo., or 8 yr. 4 mo., of $156.96, which is $78.48; for 663 mo., or 5 yr. 6 mo. 20 da., of $156.96, which is $52.32; &c. = After a little practice, the final answer may be read at once. Thus, The interest of $156.96 for 100 mo., or 8 yr. 4 mo., is $78.48; for 66 mo., or 5 yr. 6 mo. 20 da., is $52.32; &c. What is the interest for each of the above-named times of, 8. What is the interest of $36 for 3 yr. 4 mo.? 10. What is the interest of $75 for 2 yr. 9 mo. 10 da. ? 15. What is the interest of $500 for 66 16. What is the interest of $42.24 for 1 1 mo. ? yr. 15 da.? yr. 1 mo.? mo.? 17 What is the interest of $150 for 6 mo. 20 da.? 22. What is the interest of $288 for 10 da.? 23. What is the interest of $96.34 for 20 da.? 24. What is the interest of $675 for 2 da.? 25. What is the interest of $438.74 for 3 yr. 4 mo. ? 26. What is the interest of $73.87 for 1 yr. 15 da.? 27. What is the interest of $144 for 1 yr. 1 mo. 10 da.? 28. What is the interest of $56 for 4 yr. 2 mo. ? 29. What is the interest of $1728 for 1 yr. 4 mo. 20 da. ? 30. What is the interest of $327.29 for 16 yr. 8 mo. ? 31. What is the interest of $44.20 for 10 mo. ? 32. What is the interest of $57.60 for 3 mo. 10 da.? 33. What is the interest of $43.65 for 4 mo.? 34. What is the interest of $7.65 for 1 mo. 10 da.? 35. What is the interest of $97.20 for 6 mo. 20 da. ? 36. What is the interest of $237.50 for 1 mo. ? 37. What is the interest of $541 for 5 da.? 38. What is the interest of $9741 for 6 da.? 39. What is the interest of $82.47 for 3 da. ? 40. What is the interest of $32.76 for 2 yr. 9 mo. 10 da. ? 41. What is the interest of $93.27 for 6 mo. 20 da.? 174. Interest for various Times. (a.) In computing interest for other times than those already mentioned, it is usually most convenient to divide the time into parts, as illustrated below. (b.) The student should bear in mind that in the forms of written work here, as elsewhere, the letter a, b, c, &c., are used merely to indicate how the numbers standing opposite them have been obtained. In practical work they should be omitted. 1. What is the interest of $196.72 for 8 mo. 20 da.? 3 of a = b = 6.557 = Int. for 6 mo. 20 da .01 of a c= 1.967 Int. for 2 mo. b+c=$ 8.524 Int. for 8 mo. 20 da. Since at 6 per cent the interest for 1 month equals of 1 per cent of the principal, the interest for 8 months must equal 4 per cent of the principal; and since the interest for 1 day equals of .001 of the principal, the interest for 20 days must equal 20 of .001, or .003 of the principal. Hence, the interest of $169.72 for 8 mo. 20 da. = .04 + .003} .043 of $169.72, which, found by the usual method, gives $8.525 interest for 8 mo. 20 da. = 2. What is the amount of $649.37 for 17 mo. 15 da.? a+b+c=$706.189 = Amt. for 17 mo. 15 da. = Since at 6 per cent the interest for 1 month is of 1 per cent of the principal, the interest for 17 months must equal of 1 per cent .08.085 of the principal; and since for 1 day the interest equals of .001 of the principal, for 16 days it must equal of .001, or .0023 of the principal. Hence, the interest of $649.37 for 17 mo. 15 da. = .085 + .002 = .087 of $649.37, which, found by the usual method, gives $56.819, the interest, which, added to the principal, gives the amount, $706.189. - NOTE. Many other solutions might have been given to the above questions, but as they would all involve similar principles, it is unneces sary to add them. Every question in interest admits a great variety of solutions, and the pupil should examine it carefully to determine which he will adopt. Practice will enable him to select a good method at once. One process may be applied to test the correctness of a result obtained by some other. We may remark, that, as a general thing, it is better to divide than to multiply, for in division we have to consider no denomination below the lowest we wish to have in the answer. 3. What is the interest of $857.63 for 3 mo. 16 da. ? 4. What is the interest of $875.37 for 1 mo. 26 da. ? 5. What is the interest of $93.75 for 9 mo. 29 da. ? 6. What is the interest of $178.43 for 16 mo. 14 da.? 7. What is the interest of $343.65 for 13 mo. 16 da.? 8. What is the interest of $237.64 for 19 mo. 24 da. ? 9. What is the interest of $478.96 for 17 mo. 26 da. 10. What is the interest of $375.81 for 22 mo. 15 da. ? 11. What is the interest of $58.27 for 96 mo. 20 da. ? |