ilN3S[UITIES. 215 



"To find the present Worth of a Freehold Estate ^ or an Atmui" 

 ty to continue for every at Compound Interest, 



RULE.* 



As the rate per cent, is to lool. so Is the yearly rent to 

 the value required. 



EXAMPLES. 



* The reason of this rule Is obvious : for since a year's interest 

 of the price, which is given for it, is the annuity, there can neither 

 more nor less be made of that price than of the annuity, whether 

 It be employed at simple or compound interest. 



The same thing may be shewn thus : the present worth of an 



annuity to continue forever is }- ~~-\- J- — , &c. ad infinitum, 



r r^ r* r+ 



as has been shewn before ; but the sum of this series, by the rules 



of geometrical progression. Is .. ; therefore r — i : i i: n z 



r — I 



—— , which is the rule. 

 r — I 



The following theorems shew all the varieties of this rule. 



I. — L-=r/>. II. r — I %pz=.n. III. ^ + i=:r, or -=r— -i. 

 r— I p p 



The price of a freehold estate, or annuity to continue for ever, 



at simple interest, would be expressed by — , , -{ 



i-j-r 14-2/ 



+ — h — ■• J &c. ad infuutum : but ihe sum of this sfe- 



ries is Infinite, or greater than any assignable number, \\\\ich. 

 sufficiently shews the absurdity of using simple interest in these. 



