184 ESSAY ON PROBABILITIES. 



When 000 appears in the table, the sum requisite is less 

 than ten shillings. Thus, less than ten shillings im- 

 proved for 85 years at 10 per cent., will produce a 

 thousand pounds. 



There are six primary results which will be neces- 

 sary. 



1. The present value of 1L 9 meaning that fraction of 

 a pound which will, when improved at interest, produce 

 11. in a certain number of years. Since the present 

 value of WOOL is tabulated, that of 11. is virtually so, 

 and may be found by placing the decimal point before 

 any result of the preceding table. Thus, *458/. is the 

 fraction of a pound which will, when improved at 5 per 

 cent, compound interest for sixteen years, produce 11.; or, 

 in technical language, the present value of 11. due sixteen 

 years hence, at 5 per cent. To find the present value 

 for any year not in the table, multiply the present 

 values for any years in the table the sum of which is 

 the number of years in question. Thus, to find the 

 present value of 11. due fifty-seven years hence, at 3 per 

 cent., multiply together '337 and *96l, the present 

 values for fifty-five and two years, the result of which 

 is *324, the fraction of 11. required. 



2. The present value of a perpetuity of I/., or the 

 sum which will, wj^en improved at interest, pay 11. at 

 the end of every 3 65 days from the present time, for 

 ever. The number of pounds required is found by 

 dividing 1001. by the rate of interest ; being, in fact, 

 nothing but the sum which will at interest produce 11. 

 per annum. The results are in the following table : 



Rate P.V. of Perp. I Rate P.V. of Perp. Rate P.V. of Perp, 



3 



50 

 40 



25 

 J 22f 

 20 



9 11 9 

 10 10 



Thus 20J. improved at 5 per cent, yields 11. a year foi 

 ever, provided the first payment be due at the interval 

 of a year from the time of putting the money out at 



