Find the value of (x)

Question

( 1+ x / 365 )^365 -1 = ( 1+ 0.16 / 2 )^2 -1

Answer 1

It's not clear if the -1's are part of the exponent or not.  I'm assuming they are not.  The technique works the same either way.

 

( 1+ x / 365 )³⁶⁵ -1 = ( 1+ 0.16 / 2 )² -1

( 1+ x / 365 )³⁶⁵ = ( 1+ 0.16 / 2 )²

( 1+ x / 365 )³⁶⁵ = (1.08)²

( 1+ x / 365 )³⁶⁵ = 1.1664

1 + x/365 = (1.1664)^1/365

1 + x/365 = 1.000417

x/365 = 2.000417

x = 730.154