Yolanda deposited $$ \$ 4000 $$ into an account with $$ 3.6 \% $$ interest, compounded monthly. Assuming that no withdrawals are made, how much will she have in the account after 8 years? Do not round any intermediate computations, and round your answer to the nearest cent.

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To calculate the amount in the account after 8 years with monthly compounding interest, we can use the formula for compound interest:

$$
A = P \left(1 + \frac{r}{n}\right)^{nt}
$$

Where:
- $$ A $$ is the amount of money accumulated after n years, including interest.
- $$ P $$ is the principal amount (the initial amount of money).
- $$ r $$ is the annual interest rate (decimal).
- $$ n $$ is the number of times that interest is compounded per year.
- $$ t $$ is the number of years the money is invested or borrowed.

Given:
- $$ P = 4000 $$
- $$ r = 3.6\% = 0.036 $$
- $$ n = 12 $$ (since the interest is compounded monthly)
- $$ t = 8 $$

Now, we can substitute these values into the formula:

$$
A = 4000 \left(1 + \frac{0.036}{12}\right)^{12 \times 8}
$$

Let's calculate the expression step by step.

1. Calculate $$ \frac{r}{n} $$:
   $$
   \frac{0.036}{12}
   $$

2. Calculate $$ nt $$:
   $$
   12 \times 8
   $$

3. Substitute these values back into the formula and calculate $$ A $$.

Let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$12\times 8$$
- step1: Multiply the numbers:
  $$96$$
Calculate or simplify the expression $$ 0.036/12 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.036}{12}$$
- step1: Convert the expressions:
  $$\frac{\frac{9}{250}}{12}$$
- step2: Multiply by the reciprocal:
  $$\frac{9}{250}\times \frac{1}{12}$$
- step3: Reduce the numbers:
  $$\frac{3}{250}\times \frac{1}{4}$$
- step4: Multiply the fractions:
  $$\frac{3}{250\times 4}$$
- step5: Multiply:
  $$\frac{3}{1000}$$
Calculate or simplify the expression $$ 4000*(1+0.003)^96 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4000\left(1+0.003\right)^{96}$$
- step1: Add the numbers:
  $$4000\times 1.003^{96}$$
- step2: Convert the expressions:
  $$4000\left(\frac{1003}{1000}\right)^{96}$$
- step3: Simplify:
  $$4000\times \frac{1003^{96}}{1000^{96}}$$
- step4: Rewrite the expression:
  $$1000\times 4\times \frac{1003^{96}}{1000^{96}}$$
- step5: Reduce the numbers:
  $$4\times \frac{1003^{96}}{1000^{95}}$$
- step6: Rewrite the expression:
  $$4\times \frac{1003^{96}}{8^{95}\times 125^{95}}$$
- step7: Rewrite the expression:
  $$2^{2}\times \frac{1003^{96}}{2^{285}\times 125^{95}}$$
- step8: Reduce the numbers:
  $$1\times \frac{1003^{96}}{2^{283}\times 125^{95}}$$
- step9: Multiply the fractions:
  $$\frac{1003^{96}}{2^{283}\times 125^{95}}$$
Now that we have the necessary calculations:

1. The monthly interest rate $$ \frac{r}{n} = 0.003 $$.
2. The total number of compounding periods $$ nt = 96 $$.

We can substitute these values into the compound interest formula:

$$
A = 4000 \left(1 + 0.003\right)^{96}
$$

Calculating this gives us:

$$
A \approx 4000 \times (1.003)^{96} \approx 5332.73
$$

Finally, rounding to the nearest cent, Yolanda will have approximately:

$$
\boxed{5332.73}
$$

in her account after 8 years.
After 8 years, Yolanda will have approximately \$5,332.73 in her account.

Yolanda deposited \( \$ 4000 \) into an account with \( 3.6 \% \) interest, compounded monthly. Assuming that no withdrawals are made, how much will she have in the account after 8 years? Do not round any intermediate computations, and round your answer to the nearest cent.

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