If \( \$ 8,000 \) is invested in an account for 20 years. Find the value of the investment at the end of 20 years if the interest is: (a) \( 6 \% \) simple interest: \( \$ \square \) (b) \( 6 \% \) compounded annually: \( \$ \square \)

To calculate the value of the investment at the end of 20 years, we can use the formulas for simple interest and compound interest. For simple interest, the formula is: \[ A = P + (P \times r \times t) \] Where: - \( A \) is the total amount - \( P \) is the principal amount (\$8,000) - \( r \) is the interest rate (6% or 0.06) - \( t \) is the time in years (20) Plugging in the values: \[ A = 8000 + (8000 \times 0.06 \times 20) = 8000 + (8000 \times 1.2) = 8000 + 9600 = 17600 \] So for part (a), the value of the investment with simple interest is: \(\$ 17,600\) For compound interest, the formula is: \[ A = P(1 + r)^t \] Using the same values: \[ A = 8000(1 + 0.06)^{20} = 8000(1.06)^{20} \] Calculating \( (1.06)^{20} \) gives approximately \( 3.207135472 \), so: \[ A \approx 8000 \times 3.207135472 \approx 25657.08 \] Thus, for part (b), the value of the investment with compound interest is: \(\$ 25,657.08\)