In the formula below, i is the effective interest rate per period. FV and PV represent the future and present value of a sum. n represents the number of periods.

therefore, to double  FV = 2 PV

therefore     2 PV  = PV ( 1 + i )^n

 therefore    2  =  ( 1 + i )^n

Applying log on both sides,

    log2  = log( 1 + i )^n

n = (log2)/ log(1+i) 

Given i is 7%

Therefore n = log2/log1.07 = 10.245 days