10. $[-/0.83$ Points $]$
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TAMUBUSMATH 6.1.017. 0/6 Submissions Used
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You decided to invest into a mutual fund that pays 3\% per year, compounded monthly. How much should you invest now so that after 5 years from now, you will have $\mathrm{\$}2,000$ in the account? (Round your answer to the nearest cent.)

You should invest $
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Step 1 ：The problem is asking for the present value of an investment that will grow to $2000 in 5 years with an annual interest rate of 3% compounded monthly.

Step 2 ：The formula for the present value is: $PV=\frac{FV}{(1+\frac{r}{n}{)}^{nt}}$, where: \n- PV is the present value (the amount to invest now) \n- FV is the future value ($2000) \n- r is the annual interest rate (3% or 0.03) \n- n is the number of times the interest is compounded per year (12 for monthly) \n- t is the time in years (5)

Step 3 ：Substitute the given values into the formula: \nFV = 2000 \nr = 0.03 \nn = 12 \nt = 5

Step 4 ：Calculate the present value: $PV=\frac{2000}{(1+\frac{0.03}{12}{)}^{12\ast 5}}=1721.738211565979$

Step 5 ：Round the present value to the nearest cent to get the final answer: $\boxed{{\displaystyle 1721.74}}$