A four-year TIPS bond promises a real annual coupon return of 4 percent and
its face value is $1,000. While the annual inflation rate was approximately
zero when the bond was first issued, the inflation rate suddenly accelerated to
3 percent and is expected to remain at that level for the bond’s four-year term.
What will be the amount of interest paid in nominal dollars each year of the
bond’s life? What will be the face (nominal) value of the bond at the end of each
year of its life?
To calculate the amount of interest paid in nominal dollars each year of the bond's life, we need to determine the coupon payment and adjust it for inflation each year.
1. Calculate the coupon payment: The bond promises a real annual coupon return of 4 percent, based on its face value of $1,000. Therefore, the coupon payment each year will be 4 percent of $1,000, which is $40.
2. Adjust the coupon payment for inflation: The annual inflation rate is 3 percent for the bond's four-year term. This means that each year, the coupon payment will increase by 3 percent to account for inflation.
- For the first year: $40 (coupon payment) + 3% * $40 = $40 + $1.20 = $41.20
- For the second year: $41.20 (previous coupon payment) + 3% * $41.20 = $41.20 + $1.24 = $42.44
- For the third year: $42.44 (previous coupon payment) + 3% * $42.44 = $42.44 + $1.27 = $43.71
- For the fourth year: $43.71 (previous coupon payment) + 3% * $43.71 = $43.71 + $1.31 = $45.02
Therefore, the amount of interest paid in nominal dollars each year of the bond's life will be:
- Year 1: $41.20
- Year 2: $42.44
- Year 3: $43.71
- Year 4: $45.02
To calculate the face (nominal) value of the bond at the end of each year of its life, we need to adjust the face value for inflation.
- For the first year, when the inflation rate is zero, the face value remains the same at $1,000.
From the second year onwards, each year's face value will be adjusted for inflation using the annual inflation rate of 3 percent.
- For the second year: $1,000 (previous face value) + 3% * $1,000 = $1,000 + $30 = $1,030
- For the third year: $1,030 (previous face value) + 3% * $1,030 = $1,030 + $30.90 = $1,060.90
- For the fourth year: $1,060.90 (previous face value) + 3% * $1,060.90 = $1,060.90 + $31.83 = $1,092.73
Therefore, the face (nominal) value of the bond at the end of each year of its life will be:
- Year 1: $1,000
- Year 2: $1,030
- Year 3: $1,060.90
- Year 4: $1,092.73