150 On the Method of Calculating the Increment 



as compound interest the total increment, and then add in 

 the yearly rate per cent, given by the rents. Thus £100 

 worth of land increasing at the rate of 10 per cent., and 

 producing a rental of 5 per cent., will give these figures : — 



First Year Value £100 Rent £5 



Second Year Value £110 Rent £5 10s. 



Third Year Value £121 Rent £6 Is. 



And so on. Now take the third year, when the value of 

 the land is increasing by the sum of £12 2s., while for rent 

 it produces £6 Is. The total yield of the land is £18 3s., 

 and yet if this be calculated as interest on £121, which is 

 the value of the land, and which the owner could have got 

 for his land if he chose, it will give only 15 per cent., and 

 this is the sum of 10 per cent, increment and 5 per cent, 

 interest. 



The calculation of the exact rate at which the value of 

 the land in Victoria has increased would involve the solu- 

 tion of an equation of the forty-second degree, and the 

 labour so involved would not be compensated by the degree 

 of accuracy obtained. 



The following equation will give the rate of increase in 

 the value in Victoria — 



330,629 R i0 + 77,213 £ 35 + 116,935 R™+ 



1,453,383 E 25 + 2,144,999 B 20 + 2,054,839 22 15 + 

 1,689,181 R'°+ 2,610,085 R 5 = Y 



where V is the value of all the land in the colony. 



Id this equation, in order to reduce the terms from forty 

 in number down to eight, I have grouped the land sales 

 together for periods of ^nq years, and taken the middle of 

 such periods as the average time of the sales. 



A difficulty arises in determining V. The year-book of 

 Mr. Hayter gives £65,000,000 as the total rateable property 

 of the colony, but this includes all the buildings in cities, 

 townships, or farms, together with all improvements on farm 

 or pastoral lands, and to get. the value of the land by itself 

 seems impossible. 



If the rate per cent, be taken as 5, then the above equa- 

 tion will give R=105, and the value of V is £24,000,000, 

 which is perhaps under the mark, but whenever the real 

 value of V is attained some such equation as the above must 

 be used in order to give tolerably accurate results. 



