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How much would you need to deposit in an account now in order to have $\$ 4000$ in the account in 5 years? Assume the account earns $8 \%$ interest compounded monthly. Round to the nearest cent.
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Step 1 ：Given that the amount of money accumulated after 5 years, including interest (A) is \(\$4000\), the annual interest rate (r) is \(8\%\) or \(0.08\), the number of times that interest is compounded per year (n) is \(12\) times a year, and the time the money is invested for in years (t) is \(5\) years.

Step 2 ：We need to find the principal amount (P), which is the initial amount of money that needs to be deposited.

Step 3 ：The formula for compound interest is \(A = P (1 + \frac{r}{n})^{nt}\).

Step 4 ：We can rearrange this formula to solve for P: \(P = \frac{A}{(1 + \frac{r}{n})^{nt}}\).

Step 5 ：Substituting the given values into this formula, we get \(P = \frac{4000}{(1 + \frac{0.08}{12})^{12 \times 5}}\).

Step 6 ：Solving this equation gives us \(P \approx 2684.84\).

Step 7 ：\(\boxed{P \approx 2684.84}\). Therefore, you would need to deposit approximately \$2684.84 in the account now in order to have \$4000 in the account in 5 years, assuming the account earns 8% interest compounded monthly.