Explanation:
Use the compounding formula
amount = principal ( 1 + i)^n where i is decimal interest n = years
amount/principal = (1 + i)^n take LOZG of both sides
LOG ( amount/principal ) = n LOG ( 1 + i)
[ LOG (amount/principal) ] / n = LOG ( 1 +i) now raise each side to the 10
10^( ( LOG (amount/principal) /n) = 1 + i now subtract 1 from both sides to find i ...the decimal interest