Jose deposited $\$ 4000$ into an account with $6 \%$ interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in theaccount after 10 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer
Final Answer: The amount Jose will have in the account after 10 years is approximately \(\boxed{7224.44}\)
Step 1 ：Given that Jose deposited $4000 into an account with 6% interest, compounded semiannually, we are to find how much he will have in the account after 10 years. The formula for future value (FV) in the case of compound interest is: \(FV = P * (1 + r/n)^{nt}\) where: P = principal amount (the initial amount of money), r = annual interest rate (in decimal), n = number of times that interest is compounded per year, and t = time the money is invested for in years.
Step 2 ：In this case, P = $4000, r = 6% = 0.06, n = 2 (since interest is compounded semiannually), and t = 10 years.
Step 3 ：We can plug these values into the formula to find the future value of the investment: \(FV = 4000 * (1 + 0.06/2)^{2*10}\)
Step 4 ：Calculating the above expression, we get FV = 7224.44493867766
Step 5 ：Rounding to the nearest cent, we get the final answer.
Step 6 ：Final Answer: The amount Jose will have in the account after 10 years is approximately \(\boxed{7224.44}\)
