Step 1 :Define the variables: number of coffees per week is 8, price per coffee is $4.30, annual interest rate is 3.4%, and number of years is 17.
Step 2 :Calculate the amount deposited each period, \(P\), by multiplying the number of coffees per week by the price per coffee. So, \(P = 8 \times 4.30 = \$34.40\).
Step 3 :Calculate the number of periods, \(t\), by multiplying the number of years by 4 (since there are 4 weeks in a month). So, \(t = 17 \times 4 = 68\).
Step 4 :Calculate the future value of the annuity, \(FV\), using the formula \(FV = P \times \left( \frac{(1 + \frac{annual\_interest\_rate}{4})^{4t} - 1}{\frac{annual\_interest\_rate}{4}} \right)\).
Step 5 :Substitute the values into the formula to get \(FV = 34.40 \times \left( \frac{(1 + \frac{0.034}{4})^{4 \times 68} - 1}{\frac{0.034}{4}} \right)\).
Step 6 :Calculate the future value to get \(FV = \$36409.13\).
Step 7 :Round to the nearest cent to get the final answer: Christian would have \(\boxed{\$36409.13}\) in the annuity.