1822.] the perpetual Renewal of Leases. 13 



a life may drop, by paying a proposedj^'we and an annual convenj^jj 

 tionary rent, to find the landlord's interest in the lease. * 



Rule. — Subtract the value of the best life (taken from the 

 most approved tables) from the perpetuity, then it will be 



As the value of the best life 



Is to the above difference, 



So is three times the fine for each renewal ' 



To the present value of all the sums paid for renewing. 



Which, added to the yearly conventionary rent multipHed by the 

 perpetuity, will give the present value of the landlord's interest 

 m the lease. 



When the interest is either 4 or 5 percent, the numbers in the 

 following table multiplied by the fine for renewal, and the pro- 

 duct added to the yearly conventionary rent multiphed by the 

 perpetuity, will give the landlord's interest as above : 



Where the tables Numbers corresponding Numbers corresponding 

 are kept. to 4 per cent. to 5 per cent. 



"' Carlisle 0-78936 0-57355 



France 0-94280 0-70073 



Sweden 1-00534 0-74298 



Northampton 1-24640 0-94063 



Demoivre 1-44260 M0762 



London 1-57317 1-19580 



Example 1. — A lessor grants a lease of a house to a lessee on 

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

 of renewal, subject to an annual conventionary rent of 305. an 

 heriot on the death of each life 3/. and the fine for renewal 30^. 

 required the present value of the lessor's interest in the house, 

 interest being 3^ per cent. 



Answer. — -The value of the best life, from observations made 

 in France, according to M. de Parceiux, is 20-77, the value of 



the perpetuity ?^^ == 28-57143, and 28-57143 -20-77=: 7-80143; 



then by the rule we haVe, 20-77 : 7-80143 :: 3 (3 -f 30) : 37-185, 

 the present value of all the heriots and fines, to which add 

 28-57143 X 1-5 = 42-857, and the sum 80-042 = 80/. Qs. \Qd. 

 is the present value of the lessor's interest in the house. 



Example 2. — A lease of an estate is granted on three of the 

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

 subject to an annual conventionary rent of 2/. IO5. an heriot, on 

 the death of each hfe 5/. and the fine for renewal 50/. ; required 

 the present value of the landlord's interest in the estate, the rate 

 of interest 6 per cent. 



Answer. — The value of the best life, from observations made > 



at Carlisle, is 14-526, the value of the perpetuity ^^ = 16-667, 



