Pete and Elena deposit $$ \$ 6,643.00 $$ into a savings account which earns $$ 7.29 \% $$ interest compounded annually. They want to use the money in the account to go on a trip in 2 years. How much will they be able to spend? Use the formula $$ A=P\left(1+\frac{r}{n}\right)^{n t} $$, where $$ A $$ is the balance (final amount), $$ P $$ is the principal (starting amount), $$ r $$ is the interest rate expressed as a decimal, $$ n $$ is the number of times per year that the interest is compounded, and $$ t $$ is the time in years. Round your answer to the nearest cent.

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To determine how much Pete and Elena will have in their savings account after 2 years, we'll use the compound interest formula:

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

**Where:**
- $$ A $$ = the final amount in the account
- $$ P $$ = principal amount (\$6,643.00)
- $$ r $$ = annual interest rate (7.29% or 0.0729 as a decimal)
- $$ n $$ = number of times interest is compounded per year (1 for annually)
- $$ t $$ = time in years (2 years)

**Step-by-Step Calculation:**

1. **Plug in the known values:**

$$
A = 6643 \times \left(1 + \frac{0.0729}{1}\right)^{1 \times 2}
$$

$$
A = 6643 \times (1 + 0.0729)^2
$$

2. **Calculate $$ (1 + 0.0729)^2 $$:**

$$
(1.0729)^2 = 1.151103841
$$

3. **Multiply the principal by this factor:**

$$
A = 6643 \times 1.151103841 \approx 7646.78
$$

**Final Amount:**

After 2 years, Pete and Elena will have **\$7,646.78** in their savings account.
After 2 years, Pete and Elena will have \$7,646.78 in their savings account.

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