Manually calculate the compound interest on an investment of \( \$ 2,000 \) at \( 8 \% \) interest, compounded quarterly, for 1 year. Select one: O a. \( \$ 164.87 \) b. \( \$ 160.00 \) o c. \( \$ 2,164.86 \) d. \( \$ 2,720.98 \)

To calculate the compound interest on an investment of $2,000 at 8% interest, compounded quarterly for 1 year, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \] Where: - \( A \) is the amount after the interest is compounded. - \( P \) is the principal amount (initial investment). - \( r \) is the annual interest rate (in decimal form). - \( n \) is the number of times the interest is compounded per year. - \( t \) is the time the money is invested for in years. Given: - \( P = \$2,000 \) - \( r = 8\% = 0.08 \) - \( n = 4 \) (compounded quarterly) - \( t = 1 \) year Substitute the values into the formula: \[ A = 2000 \left( 1 + \frac{0.08}{4} \right)^{4 \cdot 1} \] \[ A = 2000 \left( 1 + 0.02 \right)^{4} \] \[ A = 2000 \left( 1.02 \right)^{4} \] \[ A = 2000 \cdot 1.08243216 \] \[ A = 2164.86 \] Therefore, the compound interest on an investment of $2,000 at 8% interest, compounded quarterly for 1 year is $2164.86. The correct answer is: c. $2,164.86