Final answer:
The total annual coupon income received in year 3 for a TIPS bought at $1,000 with a 2.74% coupon rate, after accounting for inflation rates of 2.09%, 3.84%, and 2.06% over three years, is $29.70.
Step-by-step explanation:
The student's question deals with calculating the total annual coupon income from a TIPS (Treasury Inflation-Protected Security) in year 3 when inflation rates vary each year. The bond was bought at issue at par for $1,000 with a 2.74% annual coupon rate. To find the income in the third year, we need to adjust the principal amount for the inflation that occurred in each year since TIPS pay interest on the adjusted principal.
First, we adjust the principal for the first year's inflation of 2.09%:
Adjusted Principal Year 1 = $1,000 * (1 + 0.0209) = $1,020.90
Next, we adjust this new principal by the second year's inflation of 3.84%:
Adjusted Principal Year 2 = $1,020.90 * (1 + 0.0384) = $1,061.36
Then, we adjust the principal once again by the third year's inflation of 2.06% to get the principal for the third year:
Adjusted Principal Year 3 = $1,061.36 * (1 + 0.0206) = $1,083.92
Finally, we calculate the total annual coupon income for year 3 by applying the coupon rate to the adjusted principal for that year:
Total Annual Coupon Income Year 3 = $1,083.92 * 0.0274 = $29.70
Therefore, the total annual coupon income you will receive in year 3 from this TIPS bond, accounting for the inflation adjustments, is $29.70.