Question

Suppose you purchase a $1,000 TIPS on January 1, 2021. The bond carries a fixed coupon of 1 percent. Over the first two years, semiannual inflation is 4 percent, 1 percent, 2 percent, and 3 percent, respectively. For each six-month period, calculate the accrued principal and coupon payment.

Answer 1

Answer:

FOR THE FIRST SIX-MONTH PERIOD

Accrued principal = $1,040

Coupon payment = $5.20

FOR THE SECOND SIX-MONTH PERIOD

Accrued principal = $1,050.40

Coupon payment = $5.25

FOR THE THIRD SIX-MONTH PERIOD

Accrued principal = $1,071.41

Coupon payment = $5.36

FOR THE FOURTH SIX-MONTH PERIOD

Accrued principal = $1,103.55

Coupon payment = $5.52

Explanation:

These can be calculated using the following formulae:

Accrued principal = Amount or previous accrued principal * (100% + inflation rate) ...........(1)

Coupon payment = Accrued principal * (Fixed coupon rate * (6 months / 12 months))............(2)

Therefore, we have:

FOR THE FIRST SIX-MONTH PERIOD

Accrued principal = $1,000 * (100% + 4%) = $1,040

Coupon payment = $1,040 * (1% * (6 / 12)) = $5.20

FOR THE SECOND SIX-MONTH PERIOD

Accrued principal = $1,040 * (100% + 1%) = $1,050.40

Coupon payment = $1,050.40 * (1% * (6 / 12)) = $5.25

FOR THE THIRD SIX-MONTH PERIOD

Accrued principal = $1,050.40 * (100% + 2%) = $1,071.41

Coupon payment = $1,071.41 * (1% * (6 / 12)) = $5.36

FOR THE FOURTH SIX-MONTH PERIOD

Accrued principal = $1,071.41 * (100% + 3%) = $1,103.55

Coupon payment = $1,103.55  * (1% * (6 / 12)) = $5.52