Matthew invests $\$ 600$ into an account with a $2.3 \%$ 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.
Answer
Final Answer: Matthew will have \(\boxed{755}\) dollars in his account after 10 years.
Step 1 ：Define the variables: the principal amount \(P = \$600\), the annual interest rate \(r = 2.3\% = 0.023\), the number of times interest is compounded per year \(n = 4\), and the time in years \(t = 10\).
Step 2 ：Calculate the future value using the compound interest formula: \(A = P \times (1 + \frac{r}{n})^{n \times t}\).
Step 3 ：Substitute the values into the formula: \(A = 600 \times (1 + \frac{0.023}{4})^{4 \times 10}\).
Step 4 ：Round the result to the nearest dollar to get the future value of the investment.
Step 5 ：The future value of the investment is \$755.
Step 6 ：Final Answer: Matthew will have \(\boxed{755}\) dollars in his account after 10 years.
