the face value of the zero-coupon bond. 13-year bond at \( 5.4 \% \); price \( \$ 3000 \) face value will be \( \$ \square \). not round until the final answer. Then round to the nearest dollar as needed.)

To find the face value of a zero-coupon bond, you can use the formula for the present value of a bond: \[ PV = \frac{FV}{(1 + r)^n} \] Here, \(PV\) is the price of the bond (\$3000), \(FV\) is the face value, \(r\) is the annual interest rate (5.4\% or 0.054), and \(n\) is the number of years until maturity (13 years). Rearranging the formula gives us: \[ FV = PV \times (1 + r)^n \] Now let's plug in the values: \[ FV = 3000 \times (1 + 0.054)^{13} \] Calculating \( (1 + 0.054)^{13} \): \[ (1.054)^{13} \approx 1.854 \] So, \[ FV \approx 3000 \times 1.854 \approx 5562 \] After rounding to the nearest dollar, the face value of the zero-coupon bond is approximately \( \$5562 \).