$$ 1 \leftarrow $$ Use the present value formula to determine the amount to be invested now, or the present value needed. The desired accumulated amount is $$ \$ 80,000 $$ after 12 years invested in an account with $$ 6.8 \% $$ interest compounded monthly. The amount to be invested now, or the present value needed, is $$ \$ \square $$ (Round to the nearest cent as needed.)

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To find the present value (PV) needed to accumulate a desired amount in the future, we can use the present value formula for compound interest:

$$
PV = \frac{FV}{(1 + r/n)^{nt}}
$$

Where:
- $$ FV $$ is the future value (the desired accumulated amount),
- $$ r $$ is the annual interest rate (as a decimal),
- $$ n $$ is the number of times that interest is compounded per year,
- $$ t $$ is the number of years the money is invested.

Given:
- $$ FV = 80000 $$
- $$ r = 6.8\% = 0.068 $$
- $$ n = 12 $$ (monthly compounding)
- $$ t = 12 $$

Now, we can substitute these values into the formula to calculate the present value.

Let's perform the calculation step by step.

1. Calculate $$ r/n $$:
   $$
   r/n = \frac{0.068}{12}
   $$

2. Calculate $$ nt $$:
   $$
   nt = 12 \times 12
   $$

3. Substitute these values into the present value formula and calculate $$ PV $$:
   $$
   PV = \frac{80000}{(1 + r/n)^{nt}}
   $$

Now, let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$12\times 12$$
- step1: Multiply the numbers:
  $$144$$
Calculate or simplify the expression $$ 0.068/12 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.068}{12}$$
- step1: Convert the expressions:
  $$\frac{\frac{17}{250}}{12}$$
- step2: Multiply by the reciprocal:
  $$\frac{17}{250}\times \frac{1}{12}$$
- step3: Multiply the fractions:
  $$\frac{17}{250\times 12}$$
- step4: Multiply:
  $$\frac{17}{3000}$$
Calculate or simplify the expression $$ 80000/(1 + 0.00566667)^(144) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{80000}{\left(1+0.00566667\right)^{144}}$$
- step1: Add the numbers:
  $$\frac{80000}{1.00566667^{144}}$$
- step2: Convert the expressions:
  $$\frac{80000}{\left(\frac{100566667}{100000000}\right)^{144}}$$
- step3: Simplify the expression:
  $$\frac{80000}{\frac{100566667^{144}}{100000000^{144}}}$$
- step4: Rewrite the expression:
  $$\frac{80000\times 100000000^{144}}{100566667^{144}}$$
Now that we have the necessary calculations, let's summarize the steps:

1. Calculate $$ r/n $$:
   $$
   r/n = \frac{0.068}{12} \approx 0.00566667
   $$

2. Calculate $$ nt $$:
   $$
   nt = 12 \times 12 = 144
   $$

3. Substitute these values into the present value formula:
   $$
   PV = \frac{80000}{(1 + 0.00566667)^{144}}
   $$

4. Calculate $$ PV $$:
   $$
   PV \approx \frac{80000}{(1.00566667)^{144}} \approx 35457.31
   $$

Thus, the amount to be invested now, or the present value needed, is approximately $$ \$ 35,457.31 $$.

So, the final answer is:
$$
\text{The amount to be invested now is } \$ 35,457.31.
$$
The amount to be invested now is \$35,457.31.

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