pur 393. The Commercial Year and Ordinary Interest. — For the pose of computing interest for short periods the so-called commercial year is usually used. Each month is counted as 30 days and the year as 360 days, or 12 months of 30 days each. Interest computed on this basis is called ordinary interest or bankers' interest. 394. The Six Per Cent Principle. Six per cent for one year is the same rate as one per cent for two months. This is a fundamental principle which forms the basis for the most important methods for computing interest when the time is expressed in days or in months and days. Under this principle the interest at 6% for two months is obtained by pointing off two places in the principal. 395. Bankers' Sixty Day Method. When the rate of interest is six per cent, the work may be simplified by special devices as is shown in the following examples. Example 1.. Find the interest on $2460 at 6% for 7 months. A vertical line is used to separate dollars and cents. Pointing off two places gives the interest for 2 months. Multiplying by 3 gives the interest for 6 months, etc. Example 2. Find interest on $780 at 6% for 35 days. Example 3. Find interest on $9300 at 6% for 2 days. Solution. 9300 interest for 60 days 310 interest for 2 days (3 of 60 days) Example 4. Find the interest on $8460 at 6% for 19 days. WRITTEN EXERCISES Using the bankers' sixty-day method, find the interest in each of the following examples, the rate in each case being six per cent. 396. Table for Bankers' Sixty-day Method. In using the bankers' sixty-day method, much depends on the skill with which the interest for a certain number of days is obtained from the interest for 60 days. Thus it is difficult to find the interest direct for 7 days, since this involves multiplying by. It is easy, however, to get the interest for 6 days (of 60) and then add to it the interest for one day (of the interest for 6 days). The interest for any number of days may be found in several ways. Thus 8 days = 6 days + 2 days = 10 days - 2 days. The following table is merely suggestive. In many cases other combinations may be equally simple. 1-30. Find the interest at 6% on $189.40 for 1 day, 2 days, etc., up to 30 days. Suggestion. To divide 189.40 by 60 simply divide by 6 and start writing the numbers one place toward the right. In similar manner divide by 30 and by 20. 31-60. Find the interest on $91400 at 6% for 31 days, 32 days, etc., up to 60 days. Suggestion. First make a table like the one above for the numbers 31 to 60. 30+ 2, etc. It is important to notice that = That is, 31 6 is of 60, that 36 30+ 1, 32 = 397. Checking. The bankers' six per cent method lends itself readily to checking. Example. Find the interest on $3940 at 6% for 37 days. Find the interest of the following and check each, the interest being 398. Finding Interest at Rates Other than Six Per Cent. - To find interest at other rates than six per cent by the bankers' sixtyday method, first find the interest at six per cent. The following examples illustrate the method. Example 1. Find the interest on $2370 at 5% for 52 days. The interest at 5% is found by deducting one-sixth of the interest at 6%. Example 2. Find the interest on $1270 for 74 days at 41%. The interest at 41% is found by deducting of the interest at 6%. Example 3. Find the interest on $7850 for 70 days at 6%. In this manner the interest can be found very simply for any of the rates which are generally prevalent. Thus, to find interest at 4%, find the interest at 6% and deduct of it. Similarly: For 8% add for 9% add for 10% add ? for 7 % add for 71% add for 5% subtract There are, however, many rates of interest for which this method is somewhat complicated. Thus to find interest at 43% we should have to subtract to get the interest at 41% and then add of 6% (of 1%) to get the required interest. To find interest at 63% we should add and then subtract 24. |