QUESTION $1 \cdot 1$ POINT
Steve invests $\$ 200$ into an account with a $2.6 \%$ interest rate that is compounded quarterly. How much money will he have in this account if he keeps it for 10 years?
Round your answer to the nearest dollar.
Provide your answer below:
$\$ \square$
Answer
Final Answer: \(\boxed{259}\) dollars.
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.
