Problem
For each deposit, find the future value (that is, the final amount on deposit) when compounding occurs (a) annually, (b) semiannually, and (c) quarterly. \begin{tabular}{ccc} Principal & Rate & Time \\ $\$ 7000$ & $5 \%$ & 6 years \end{tabular} (a) If it is compounded annually, what is the amount after 6 years? \[ A=\$ 9380.67 \] (Do not round until the final answer. Then round to the nearest cent as needed.) (b) If it is compounded semiannually, what is the amount after 6 years? \[ A=\$ 9414.22 \] (Do not round until the final answer. Then round to the nearest cent as needed.) (c) If it is compounded quarterly, what is the amount after 6 years? \[ A=\$ \square \] (Do not round until the final answer. Then round to the nearest cent as needed.) Get more help Clear all Check answer
Solution
Step 1 ：Define the variables: the principal amount \(P = \$7000\), the annual interest rate \(r = 0.05\), and the time in years \(t = 6\).
Step 2 ：Calculate the future value for quarterly compounding. The number of times interest is compounded per year \(n = 4\).
Step 3 ：Use the formula for future value \(FV = P \times (1 + r/n)^{n \times t}\).
Step 4 ：Substitute the values into the formula: \(FV = 7000 \times (1 + 0.05/4)^{4 \times 6}\).
Step 5 ：Calculate the future value to get \(FV = 9431.45735290045\).
Step 6 ：Round the future value to the nearest cent to get \$9431.46.
Step 7 ：Final Answer: The future value of the deposit when compounded quarterly after 6 years is \$9431.46. Therefore, the final answer is \(\boxed{9431.46}\).
