Diego and Layla deposit \( \$ 964.00 \) into a savings account which earns \( 14.6 \% \) interest compounded quarterly. They want to use the money in the account to go on a trip in 3 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. \( \$ \square \)

To find out how much Diego and Layla will have in their savings account after 3 years with a principal of \( \$964.00 \), an interest rate of \( 14.6\% \) compounded quarterly, we can use the formula given: - \( A = P\left(1+\frac{r}{n}\right)^{nt} \) Where: - \( P = 964.00 \) - \( r = 14.6\% = 0.146 \) - \( n = 4 \) (quarterly) - \( t = 3 \) Plugging in the values: 1. Calculate \( \frac{r}{n} = \frac{0.146}{4} = 0.0365 \) 2. Calculate \( nt = 4 \times 3 = 12 \) Now, describe the formula: \[ A = 964 \left(1 + 0.0365\right)^{12} \] \[ A = 964 \left(1.0365\right)^{12} \] Calculating \( (1.0365)^{12} \): \[ (1.0365)^{12} \approx 1.4863 \] Now, multiply by the principal \( P \): \[ A \approx 964 \times 1.4863 \approx 1434.98 \] So, rounding to the nearest cent: \[ A \approx \$1434.98 \] Diego and Layla will be able to spend approximately \( \$1434.98 \) on their trip!