Problem $2$

Consider an investor who, on January $1,2014,$ purchases a TIPS bond with an original principal of $$100,000,$ an $8\%$ annual coupon rate, and $10$ years to maturity.

a$.$ If the semiannual inflation rate during the first six months is $0\mathrm{.}3\%,$ calculate the principal amount used to determine the first coupon payment and the first coupon payment $($paid on June $30,2014).$

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 $1\%.$ Calculate the inflation adjusted principal at the end of the second six months $($on December $31,2014)$ and the coupon payment to the investor for the second six$-$month period. What is the inflation$-$adjusted principal on this coupon payment date?