year, the interest on $1 for 2 months, is of $0.06= $0.01. Again, since 6 days is when we reckon 30 days to each of 2 months, month, it follows that the interest on $1, for 6 days, is of $0.01=$0.001. Hence, we have the following RULE. Call half the number of months, CENTS; one-sixth the number of days, MILLS. EXAMPLES. 1. What is the interest of $1 for 7 months and 10 days, at 6 per cent.? In this example, half the number of months is 31; which, being called cents, gives $0.035 for the interest of $1 for 7 months; again, one-sixth of the number of days is 1, which, being called mills, gives $0.001 for the interest of $1 for 10 days; therefore, the interest for $1, for 7 months and 10 days, is $0.035+$0·001= $0.0363. 2. What is the interest of $1 for 11 months and 11 days, at 6 per cent. ? Ans. $0.056. 3. What is the interest of $1 for 3 years, 7 months, that is, for 43 months, at 6 per cent.? Ans. $0.215. 4. What is the interest of $1 for 2 years, 7 months, Ans. $0.1565. 5. What is the interest of $1 for 1 year, 7 months, Ans. $0.0975. 6. What is the interest of $1 for 7 years and 9 days, Ans. $0-4215 and 9 days, at 6 per cent.? and 15 days, at 6 per cent.? at 6 per cent.? Case II. To find the interest of any given principal, for any given time, at 6 per cent., we have this RULE. Find the interest on $1 for the given time, by Case I., Art. 63. Then multiply the interest thus found by the number of dollars in the given principal. 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, 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 days, at 6 per cent.? years and 9 Ans. $143 786295. 4. What is the interest of $100 for months, at 6 per cent.? 5. What is the interest of $59103 months, and 7 days, at 6 per cent.? 16 years and 8 Ans. $100. for 4 years, 3 Ans. $151.402185. 6. What is the interest of $0∙134 for 4 months and 3 days, at 6 per cent.? Ans. $0.002747. Case III. To find the interest on any given principal, for any given time, at any given rate per cent., we have this RULE. Find the interest on the given principal, for the given time, at 6 per cent., by Case II., Art. 63. Then increase, or decrease, this interest by the same part of itself as it would be necessary to increase, or decrease 6, in order to make it agree with the given rate per cent. EXAMPLES. 1. What is the interest of $19.41 for 1 year, 7 months, and 13 days, at 7 per cent.? In this example, we find, by Case II., that the interest of $19.41 for 1 year, 7 months, and 13 days, at 6 per cent., is $1.886005. Since 6, increased by its sixth part, equals 7, it will be necessary to increase the interest just found, for 6 per cent., by its sixth part, which thus becomes $2.2003391, for the interest at 7 per cent. 2. What is the interest of $530 for 3 years and 6 months, at 5 per cent.? Ans. $92.75. In this example, it was necessary to decrease the interest at 6 per cent. by its sixth part. days, at 8 per cent.? 3. What is the interest of $5.37 for 4 years and 12 Ans. $1.73272. In this example, we increased the interest at 6 per cent. by its third part. 4. What is the interest of $4070 for 3 months, at 9 per cent.? Ans. $91.575. 5. What is the interest of $3671 for 6 months, at 10 per cent.? Ans. $183.55. 6. What is the interest of $4920.05 for 3 months, at 4 per cent.? Ans. $49.2005. 7. What is the interest of $40.17 for 3 months and 18 days, at 3 per cent.? Ans. $0.36153. 8. What is the interest of $37.13 for 5 months and 12 days, at 4 per cent.? Ans. $0.7518825. NOTE. When the principal is given in English money, we must reduce the shillings, pence, and farthings to the decimal of a pound, and then proceed as in Federal money. 9. What is the interest of £75 13 s. 6 d. for 3 years and 5 months, at 6 per cent.? In this example, 13 s. 6 d., reduced to the decimal of a pound, is £0-675, so that our principal is £75.675; the interest on £1 for 3 years and 5 months, at 6 per cent., is £0 205, which, multiplied into 75-675, the number of pounds, gives £15·513375=£15 10 s. 3 d for the interest required. 10. What is the interest of £14 5 s. 31 d. for 4 years, 6 months, and 14 days, at 7 per cent.? 100 Ans. £4 10 s. 7 d., nearly. 11. What is the interest of £1 7 s. 6 d. for 2 years and 6 months, at 4 per cent.? Ans. £0 3 s. 11⁄2 d. 12. What is the interest of £105 10 s. 6 d. for 91⁄2 months, at 5 per cent.? Ans. £4 3 s. 6 d. 15 far. When the interest is 7 per cent., it may be readily computed by the assistance of the following table, which gives the interest of $1, or £1, for any time, in months and days, not exceeding 1 year. INTEREST TABLE AT SEVEN PER CENT. Days. 0 Month. 1 Month. 2 Months. 3 Months. 4 Months. 5 Months. 0 0.00000 0.00583 0.01167 0.01750 0.02333 0.02917 1 0.00019 0.00603 0.01186 0.01769 0.02353 0.02936 2 0.00039 0·00622 0·01206 0.01789 0.02372 0.02956 3 0.00058 0.00642 0·01225 0·01808 0.02392 0·02975 4 0.00078 0·00661 0·01244 0.01828 0.02411 0.02994 5 0.00097 0.00681 0.01264 0.01847 0.02431 0.03014 6 0.00117 0.00700 0.01283 0.01867 0.02450 0.03033 7 0.00136 0.00719 0.01303 0.01886 0.02469 0.03053 8 0.00156 0.00739 0.01322 0.01906 0.02489 0.03072 9 0.00175 0.00758 0.01342 0.01925 0.02508 0.03092 10 0.00194 0.00778 0.01361 0.01944 0.02528 0.03111 11 0.00214 0.00797 0.01381 0.01964 0.02547 0.03131 12 0.00233 0.00817 0.01400 0.01983 0.02567 0.03150 13 0.00253 0.00836 0.01419 0.02003 0.02586 0.03169 14 0.00272 0.00856 0.01439 0.02022 0.02606 0.03189 15 0.00292 0.00875 0.01458 0.02042 0.02625 0.03208 16 0.003110-00894 0.01478 0.02061 0.02644 0.03228 17 0.00331 0.00914 0.01497 0.02081 0.02664 0.03247 18 0.00350 0.00933 0.01517 0.02100 0.02683 0.03267 19 0.00369 0.00953 0.01536 0.02119 0.02703 0.03286 20 0.00389 0.00972 0.01556 0.02139 0.02722 0·03306 21 0.00408 0.00992 0.01575 0.02158 0.02742 0.03325 22 0.00428 0.01011 0.01594 0.02178 0.02761 0.03344 23 0.00447 0.01031 0.01614 0.02197 0.02781 0.03364 24 0.00467 0.01050 0.01633 0.02217 0.02800 0.03383 25 0.00486 0.01069 0.01653 0.02236 0.02819 0.03403 26 0.00506 0.01089 0.01672 0.02256 0.02839 0.03422 27 0.00525 0.01108 0.01692 0.02275 0.02858 0.03442 28 0.00544 0.01128 0.01711 0.02294 0.02878 0.03461 29 0.00564 0.01147 0.01731 0.02314 0.02897 0.03481 300-00583 0.01167 0.01750 0.02333 0-02917 0.03500 |