The calculation you show in your work answers a different question, namely: How much should I invest now with a one-time deposit so as to have $\$ 2000$ after six quarters?
For your stated problem, you should use the present value of annuity formula: $V=R\cdot \frac{1-(1+i)^{-n}}{i}$ where $R=\$2000$, $i=.03$, and $n=6$.