Final answer:
The first coupon payment for the Treasury inflation-protected note with an initial principal of $1,000,000 and an annual coupon rate of 2.8%, after considering the semiannual inflation rate of 1.2%, will be $14,168(option a).
Step-by-step explanation:
The question asks what the first coupon payment will be for a Treasury inflation-protected note with an original principal amount of $1,000,000 and a 2.8 percent annual coupon rate (paid semiannually) when the semiannual inflation rate over the first six months is 1.2%. To solve this, we must first adjust the principal to reflect inflation, and then calculate the semiannual coupon payment based on the adjusted principal.
First, we adjust the principal amount for inflation:
Adjusted Principal = Original Principal × (1 + Inflation Rate)
= $1,000,000 × (1 + 0.012)
= $1,000,000 × 1.012
= $1,012,000.
Next, we calculate the semiannual coupon payment:
Semiannual Coupon Payment = Adjusted Principal × (Annual Coupon Rate / 2)
= $1,012,000 × (0.028 / 2)
= $1,012,000 × 0.014
= $14,168.
Therefore, the first coupon payment will be $14,168, which corresponds to option (a).