5. ## Re: investment

Very unclear question.

25000(1 + i)^1.5 = 27500
(1 + i)^1.5 = 27500/25000
1 + i = (27500/25000)^(1/1.5) : remember that if a^p = b, then a = b^(1/p)
i = (27500/25000)^(1/1.5) - 1
i = .0656... : so annual rate = ~6.56%

Your 6 2/3% result assumes SIMPLE interest; if so, then SHOULD be specified in the problem statement.