What is the discount on a bill of £138. 14. 4, due 2 years hence, discount being at 4½ per cent?
Answer, £11. 9. 1.
What is the present value of £1031. 17, due 6 months hence, interest being at 3 per cent?
Answer, £1016. 12.
253. If we multiply by a + b, or by a-b, when we should multiply by a, the result is wrong by the fraction
| b | + b, or | b | , |
| a | a - b |
of itself: being too great in the first case, and too small in the second. Again, if we divide by a + b, where we should have divided by a, the result is too small by the fraction b/a of itself; while, if we divide by a-b instead of a, the result is too great by the same fraction of itself. Thus, if we divide by 20 instead of 17, the result is ³/₁₇ of itself too small; and if we divide by 360 instead of 365, the result is too great by ⁵/₃₆₅, or ¹/₇₃ of itself.
If, then, we wish to find the interest of a sum of money for a portion of a year, and have not the assistance of tables, it will be found convenient to suppose the year to contain only 360 days, in which case its 73d part (the 72d part will generally do) must be subtracted from the result, to make the alteration of 360 into 365. The number 360 has so large a number of divisors, that the rule of Practice (230) may always be readily applied. Thus, it is required to find the portion which belongs to 274 days, the yearly interest being £18. 9. 10, or 18·491.
| 274 | 18·491 | |
| 180 | is ½ of 360 | 9·246 |
| 94 | ||
| 90 | is ½ of 180 | 4·623 |
| 4 | is ¹/₉₀ of 360 | ·205 |
| 9)14·074 | ||
| 8)1·564 | ||
| ·196 | ||
13·878 = £13 . 17 . 7 Answer.