\( \$ 1,500 \) are deposited into an account with a \( 5 \% \) interest rate, compounded annually (1 time per year). Find the accumulated amount after 15 years. Hint: \( A=P\left(1+\frac{r}{k}\right)^{k t} \) Round your answer to the nearest cent (hundredth

To find the accumulated amount after 15 years with an initial deposit of \( P = 1500 \), an interest rate \( r = 0.05 \), compounded annually \( k = 1 \), and time \( t = 15 \), we can use the formula: \[ A = P\left(1+\frac{r}{k}\right)^{kt} \] Substituting the values: \[ A = 1500\left(1+\frac{0.05}{1}\right)^{1 \cdot 15} \] \[ A = 1500\left(1 + 0.05\right)^{15} \] \[ A = 1500\left(1.05\right)^{15} \] Calculating \( (1.05)^{15} \): \[ (1.05)^{15} \approx 2.07893 \] Now substituting back: \[ A \approx 1500 \times 2.07893 \approx 3118.39 \] Rounding to the nearest cent, the accumulated amount after 15 years is approximately \( \$ 3,118.39 \).