$3,000 after 5 years at an interest rate of 3.0 % is the nearest cent.

You didn't say whether the 3% interest is simple interest, or compound interest, or how often it's compounded.  Each type of interest leads to a different answer.

-- If it's 3.0% simple interest, then your money earns

                                     (3.0 x 5) = 15%
 
in 5 years.  At the end of the 5 years, your investment would be worth

                             (1.15 x 3000) = $3450.

-- If the 3.0% is compounded annually, then in 5 years your money earns

                           (1.03)⁵ = 1 + 15.93%

and the original investment is worth  (3000 x 1.1593) = $3,477.82 .