PROBLEM: What is the interest on $320 for 7 mo. 20 da. at 6%. In the majority of states, the legal rate of interest is 6%, so it is important that the pupil understands this method. There is another reason, too, why he should know the 6% method. He can use it to advantage with other rates, by dividing the interest for the given time at 6% by 6, and then multiplying by the given rate per cent. PROBLEM: What is the interest on $360 for 2 yr. 2 mo. 5 da. at 7% ? Use the 6% method. The interest on $1 for 2 yr. 2 mo. 5 da. = $.130%. The interest on $360 is 360 x $.130 at 6% = $47.10. Remember: = at 1% 7.85. at 7% $54.95. = To get the interest at any rate, using the 6% method, Divide the interest at 6% for the given time by 6, and multiply by the given rate per cent. 60-DAY METHOD. The 60-day method is used quite extensively by business men. It is the 6% method improved with a few short cuts, By it the interest is ascertained first for 2 mo., by getting of the principal. Call the given times in days, months, and years, fractional parts of 2 mo., and the interest is then easily deduced from the interest for 60 days. PROBLEM: Find the interest on $500 for 1 yr. 4 mo. 20 da. at 6%. WORK: $500.00 Principal. 5.00 Int. for 2 mo. ( of Prin.). $40.00 Int. for 16 mo. (8 x $5). 1.67 Int. for 20 da. (of 60 da.). $41.67 Int. for 16 mo. 20 da. Give the pupil many problems to be worked by the 60-day method. Not all are so easy as the one given above. The thing desired is skill in finding the desired fractional parts of 2 mo. or 60 da. If another rate than 6% is given, find the interest for the given time at 6%, then for the given rate, a before explained. METHODS OF RECKONING TIME. 1. The Common Method: When the time is long, generally 30 days are con sidered a month. 2. The Exact Method: When the time is short, the exact number of days is generally counted but we sometimes find the exact number of days also when the time is long. 3. The Banker's Method: Bankers get the exact number of days between two dates, but each day is reckoned as to of a year. 1. Finding the difference in time when the time is long : PROBLEM: Find the time between April 12, 1895, and Sept. 22, 1899. BEST METhod. From April 12, 1895 to April 12, 1899 is 4 yr. = NOTE.- If the rate and principal are given, it is a simple matter to find the interest, now that we have the time. EXPLANATION: The results by these two methods do not always agree, but they never vary by more than 2 days. The difference lies in the fact that in the first method we find first the whole number of years, then whole number of months, then days; while in the latter method, we call every month 30 days, when in fact some have more, some less. In actual work, the first method is carried out in the head, with little or no written work. 2. Finding the difference in time when the time is short: PROBLEM: Find the difference in time between April 12 and July 15, 1902. NOTE. If the rate and principal are given now, it is a simple matter to find the interest. Although exact time is generally found only when the time is short, yet sometimes we find the exact number of days when the time is long. The following table gives the exact time in days between two dates. If February of a leap year is included, count an additional day. The day of the date of any note is not included. EXACT-TIME TABLE JAN FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. Ост. Nov. DEC. 107 137 108 138 19 50 78 109 139 20 51 79 110 21 52 80 111 22 53 81 112 142 173 203 119 151 168 198 229 260 169 199 230 261 170 200 231 262 292 323 140 171 201 232 263 293 141 172 202 233 264 294 325 234 113 143 174 204 235 266 296 327 114 144 175 205 236 267 297 115 145 176 206 237 268 298 329 116 146 177 207 238 269 299 330 260 117 147 178 208 239 270 300 331 361 118 148 179 209 240 271 301 332 30 149 180 210 241 272 302 333 363 120 150 181 211 242 273 303 364 212 243 290 321 351 HOW TO USE THE EXACT-TIME TABLE. Suppose we wish to get the exact time between the two dates given in the last problem, that is, from April 12 to July 15, 1902. April 12 is numbered 102. July 15 is numbered 196. - = 196 102 94. 94 includes the last day but not the first. Result, 94 da. Practice using the table. THE THREE CLASSES OF INTEREST PROBLEMS. There are only three classes of problems in interest. Only one illustration of the work necessary will be given under each class, but many others may be taken from the pupil's text-book. I. To find the Rate, when Principal, Interest, and Time are given. PROBLEM: What will be the rate on $300 to gain $20.25 in 1 yr. 6 mo. ? Divide the interest by the interest on the principal for the given time at 1%. II. To find the Principal, when Amount, Rate, and Time are given. PROBLEM: What principal at 5% will amount to $319 in 1 vr. 3 mo. 6 da.? |