Consider an investor who, on January 1, 2019, purchases a TIPS bond with an original principal of $116,000, an 10 percent annual (or 5 percent semiannual) coupon rate, and 15 years to maturity. a. If the semiannual inflation rate during the first six months is 0.4 percent, calculate the principal amount used to determine the first coupon payment and the first coupon payment (paid on June 30, 2019). b. From your answer to part a, calculate the inflation-adjusted principal at the beginning of the second six months. c. Suppose that the semiannual inflation rate for the second six-month period is 1.0 percent. Calculate the inflation-adjusted principal at the end of the second six months (on December 31, 2019) and the coupon payment to the investor for the second six-month period.

(a) $5,823.20

(b) $116,464.

(c) $5,881.43.

Explanation:

Given that,

Original principal = $116,000

Interest rate = 0.5% semi-annual

Time period = 10 years

Inflation rate = 0.4% semi-annual

(b) Inflation adjusted premium at the end of 6 months on June 30,2019:

= Original principal * Semi-annual inflation rate

= $116,000 * (1 + 0.004)

= $116,464.

Therefore, the inflation adjust principal at the beginning of six months is $116,464.

(a) First coupon payment paid on June 30,2019:

= inflation adjust principal * Interest rate

= $116,464 * 0.05

= $5,823.20

(c) Inflation adjusted premium at the end of 6 months on December 31,2019:

= Principal in June 30,2019 * Semi-annual inflation rate

= $116,464 * (1 + 0.01)

= $117,628.64.

Coupon payment on December 31,2019:

= Inflation adjusted premium * Interest rate

= $117,628.64 * 0.05

= $5,881.43.