How much money should be deposited today in an account that earns $4.5 \%$ compounded monthly so that it will accumulate to $\$ 15,000$ in 2 years?
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The amount of money that should be deposited is $\$ \square$. (Round up to the nearest cent as needed.)

Step 1 ：The problem is asking for the present value of an investment, given the future value, interest rate, and time period. The formula for present value when interest is compounded monthly is: \(PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}\) where: PV is the present value (the amount of money to be deposited today), FV is the future value ($15,000 in this case), r is the annual interest rate (4.5% or 0.045 in this case), n is the number of times interest is compounded per year (12 times in this case, since it's compounded monthly), t is the time in years (2 years in this case).

Step 2 ：We can plug in the given values into this formula to find the present value. \(FV = 15000\), \(r = 0.045\), \(n = 12\), \(t = 2\)

Step 3 ：Calculate the present value: \(PV = \frac{15000}{(1 + \frac{0.045}{12})^{12*2}}\)

Step 4 ：Final Answer: The amount of money that should be deposited today is approximately \(\boxed{13711.28}\).