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.

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.