A P 1 rnnt Show that t 1n APn middot 1n1 rnSolutionA P

A = P (1 + r/n)^nt Show that t = 1n (A/P)/n middot 1n(1 + r/n)

Solution

A = P ( 1+ r/n ) ^nt

dividing entire equation by P

A/P = ( 1+ r/n ) ^nt

taking natural log on both sides

ln ( A/P ) = nt ln ( 1 + r/n)

divide both sides by ln (1 + r/n)

ln ( A/P ) / ln (1 + r/n) = nt

isolate t by dividing both sides by n

ln ( A/P ) / ln (1 + r/n) * n = t

or

t = ln ( A/P ) / n* ln (1 + r/n)