Final answer:
To determine the price of the Treasury bond, calculate the coupon payments, discount them back at the given spot rates, and sum up their present values. The bond price is calculated to be $1,001.51 after rounding to the nearest cent.
Step-by-step explanation:
To calculate the price of a one-year $1,000 par Treasury bond with a 2.1% coupon, compounded semiannually, we need to use the given six-month Treasury spot rate of 1.6% APR and the one-year rate of 2.1% APR to discount the bond's cash flows back to their present value. The bond will pay two coupons (one every six months) and the face value at the end of one year.
The semiannual coupon payment can be calculated as follows: Coupon Payment = $1,000 * 2.1% / 2 = $10.50.
The bond's cash flows consist of the first coupon payment in six months and the second coupon payment plus the face value at the end of one year. These cash flows must be discounted using the appropriate spot rates.
The present value of the first coupon payment (PV1) is: PV1 = $10.50 / (1 + 1.6%/2) ^1 = $10.33.
The present value of the second coupon payment and the face value (PV2) is: PV2 = ($10.50 + $1,000) / (1 + 2.1%/2) ^2 = $991.18.
The price of the bond is the sum of these present values: Price = PV1 + PV2 = $10.33 + $991.18 = $1,001.51. After rounding to the nearest cent, the price is $1,001.51.