14 i Mr. Adams on [Jan. 



and 16-667 - 14-526 = 2- 141; then by the rule, we have 

 'i4-626 : 2-141 :: 3 (5 + 60) : 24-32, the present value of all the 

 heriots and fines ; the conventionary rent multiplied by the per- 

 petuity is 2.i- X -g = g- = 41-666, &c. 



Therefore, 24-32 -f 41-666, &c. = 65-986 = 65/. \9s.S^d. is 

 the present value of the landlord's interest in the estate. 



Example 3. — A lease of an estate is granted on three of the 

 best lives that can be found, with a perpetual right of renewal 

 with the best lives also, subject to a fine of 200/. for each 

 renewal ; required the present value of the landlord's interest in 

 the estate, according to observations made at each of the places 

 mentioned in the foregoing table, interest being either 4 or 5 per 

 cent. 



Answer. — ^The numbers standing against Carlisle, and under 

 4 and 5 per cent, are -78936 and -57355, each of which being 

 multiphed by the fine for renewal (200/.) will produce 157-872/. 

 and 114-71/. respectively, which are the present values of the 

 landlord's interest in the estate, according to the Carlisle tables. 

 In like manner, the remaining values are found, and the whole 

 set down as under. 



According to die 4 per c«nt. 5 per cent. 



Carlisle tables 157/. 17s. d^d 1 14/. 14.s. 2^d. 



French tables 188 11 2^ ....140 2 11 



Swedish tables 201 1 4i- ....148 11 11 



Northampton tables. . . 249 5 7 188 2 6± 



Demoivre's hypothesis. 288 10 4i 221 10 5|- 



London tables 314 12 8 .... 239 3 2^ 



Although the last two mentioned tables are not much used at 

 present, yet seeing the different results produced by the preced- 

 ing four, it would, in my opinion, be proper to advise such per- 

 sons who may have occasion to make bargains wherein the 

 probabihties of lives are concerned, to stipulate that a particular 

 table should be the ground work of their agreement; then, what- 

 ever might be the consequence, it must be abided by. 



Would not a standard set of tables of mortality be as desirable 

 and beneficial in this country, as standard tables of weights and 

 measures ? 



An approximate value of an annuity on a single life may be 

 found as follows within particular limits : 



Take half the complement of the age to 86, and find the pre- 

 sent value of 1/. per annum, which corresponds to the half 

 coroplement, and you will have the value of the given life for an 

 annuity of 1/. nearly, the rate of interest being 4 per cent. If 

 the rate of interest be 5 per cent, take half the complement of 

 the given age to 85, and proceed as above, according to the 

 Carhsle tables. 



