108 { 120; 117 { 130; 126 { 140; etc. { 12 { 13 { 14
The quotient of the difference in a regular progression, when divided by nine, gives the figures transposed, thus: 130 - 13 = 117 ÷ 9 = 13, which are the figures to be sought for when a discrepancy of 117 is shown; but this will not apply to differences below 81, nor to mixed transpositions. An error divisible by two may be caused by posting an item to the wrong side of the ledger.
Short Method to Find the Interest of a Given Sum.
Reduce the time to months, and to the number thus found annex one-third of the days, which whole number multiplied by one-half of your principal will produce you the required interest in dollars, cents and mills, at 6 per cent. If days only are given, multiply one-third of the days by one-half of the principal for the required interest at 6 per cent. Note these exercises:
$250 at 6% for 8 mos. 6 ds. = 82 × 125 = $10.25.
$250 at 6% for 93 ds. = 31 × 125 = $3.88.
$250 at 6% for 9 mos. = 9 × 125 = $11.25.
In some respects this rule is superior to the well-known 60-day method of reckoning interest.
462.50 .48 ------- 6 | 360 ---- 60 | 222.0000 | 3.70
Multiply the _principal_ (amount of money at interest) by the time, reduced to days; then divide this product by the quotient obtained by dividing 360 (the number of days in the interest year) by the per cent. of interest, and the quotient thus obtained will be the required interest. Require the interest of $462.50 for one month and eighteen days at 6 per cent. An interest month is 30 days; one month and 18 days equals 48 days. $462.50 multiplied by .48 gives $222.0000; 360 divided by 6 (the per cent. of interest) gives 60, and $222.0000 divided by 60 will give you the exact interest, which is $3.70. If the rate of interest in the above example were 12 per cent., we would divide the $222.0000 by 30 (because 360 divided by 12 gives 30); if 4 per cent., we would divide by 90; if 8 per cent., by 45; and in like manner for any other per cent.
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