If \( \$ 850 \) are deposited into an account with a \( 6 \% \) interest rate, compounded monthly, what is the balance after 7 years? \[ F=\$[?] \] \( F=P\left(1+\frac{r}{n}\right)^{n t} \) Round to the nearest cent.

To calculate the balance after 7 years with the given formula \( F = P\left(1+\frac{r}{n}\right)^{nt} \), we can substitute in the values: - \( P = 850 \) - \( r = 0.06 \) (6% as a decimal) - \( n = 12 \) (compounded monthly) - \( t = 7 \) Now substituting into the formula: \[ F = 850\left(1+\frac{0.06}{12}\right)^{12 \times 7} \] Calculating \( \frac{0.06}{12} \): \[ \frac{0.06}{12} = 0.005 \] Now substituting back into the formula: \[ F = 850\left(1 + 0.005\right)^{84} \] Calculating \( (1.005)^{84} \): \[ (1.005)^{84} \approx 1.48985 \] Now substituting this back into the formula: \[ F \approx 850 \times 1.48985 \approx 1261.3725 \] Rounding to the nearest cent, the balance after 7 years is: \[ F \approx \$1261.37 \] So, the answer is \( F=\$1261.37 \).