A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value. If the interest rate is 12% with annual compounding how much would you pay today for a zero-coupon bond with a face value of $1,600 that matures in 11 years? Please round your answer to the nearest hundredth.

To find the price of the zero-coupon bond today, we can use the formula for calculating the present value of a single sum in the future:

PV = \dfrac{FV}{(1 + r)^n}

where:
- PV is the present value of the bond
- FV is the future value or face value of the bond ($1,600)
- r is the interest rate per period (12% annual rate, so r = 0.12 )
- n is the number of periods (11 years)

Plug in the values and calculate:

PV = \dfrac{1600}{(1 + 0.12)^{11}}

PV = \dfrac{1600}{(1.12)^{11}}

PV = \dfrac{1600}{2.853116706}

PV ≈ 560.31

Therefore, you would pay approximately $560.31 today for a zero-coupon bond with a face value of $1,600 that matures in 11 years.

\boxed{PV ≈ \$560.31}