Step 1 :Define the variables: Principal amount (P) = $200, Interest rate (r) = 2.6%, Number of times interest applied per time period (n) = 4, Number of time periods the money is invested for (t) = 10 years.
Step 2 :Calculate the future value (FV) using the formula: \(FV = P \times (1 + \frac{r}{n})^{n \times t}\)
Step 3 :Substitute the values into the formula: \(FV = 200 \times (1 + \frac{0.026}{4})^{4 \times 10}\)
Step 4 :Calculate the future value: \(FV = 259.16787310873997\)
Step 5 :Round the result to the nearest dollar: \(FV_{rounded} = 259\)
Step 6 :Final Answer: \(\boxed{259}\) dollars.