THE COMPOUND INTEREST LAW 389 



If P is the principal at any time t years and compound interest 

 ;it / per cent, per annum is payable at every instant, then 

 8P) would be the principal at (t + 8t) years and 8P is the 

 interest on P for Bt years at r per cent. 



u 



: 



SP Pr 



or = ^ 



U 100 

 and when & is made infinitely small, 



dP = Pr 



dt " 100 



1-1? U+ Const 



log e P = + Const 



Let P be the principal at the beginning, then when t = 0, P = P , 



and log e P = Const. 



log e P - log, P = 



Z. _rL" 



ge P 100 

 P ^- 



plOO 



P ~ 



*0 



r< 



and P = P<f 



Example. In what time would a certain sum of money invested 

 at 2 per cent, per annum' double itself if the interest is payable 

 at every instant. 



In this example P = 2P 



rt_ 



and e lo = 2 



x 0-4343 = 0-3010 



30-10 

 ~ 0-4343r 



69-33 

 r 



= 27-73 years, when r = 2J per cent. 



