Respuesta :
To compare the two investments, we'll first calculate the future value of the investment compounded annually, and then we'll calculate the future value of the investment compounded periodically.For the investment compounded annually: Principal (P) = $2000 Annual Interest Rate (r) = 3% or 0.03 Number of Years (n) = 19Using the formula for compound interest: [A = P \times (1 + r)^n][A = 2000 \times (1 + 0.03)^{19}][A \approx 2000 \times (1.03)^{19}][A \approx 2000 \times 2.813687][A \approx 5627.37]Now, for the investment compounded periodically: Principal (P) = $2000 Annual Interest Rate (r) = 3% or 0.03 Interest Periods (m) = 2 (semi-annually) Number of Years (n) = 19Using the formula for compound interest compounded periodically: [A = P \times \left(1 + \frac{r}{m}\right)^{n \times m}][A = 2000 \times \left(1 + \frac{0.03}{2}\right)^{19 \times 2}][A \approx 2000 \times \left(1 + 0.015\right)^{38}][A \approx 2000 \times (1.015)^{38}][A \approx 2000 \times 3.23548][A \approx 6470.96]So, after 19 years, the investment compounded periodically will be worth $6470.96, which is more than the investment compounded annually at $5627.37.
