Quarterly compound interest evaluated without a calculator using a binomial expansion

A deposit of \(3000\) dollars is placed in a savings account. Interest is added every three months at a nominal rate of \(12\%\) per annum. At the end of the first year, the account holds \(3000(1+k)^4\) dollars, where \(k\) is a rational number.

1. Write down \(k\).[1]
2. Expand and simplify \((1+x)^4\).[2]
3. Hence or otherwise, find, to the nearest dollar, the balance of the account at the end of the first year.[4]