$2-$Consider an investor who, on January $1,2020,$ purchases a

principal of $$100,000,$ a $4\mathrm{.}50$ percent coupon rute with semiannual payments, and $5$ years to

maturity.

a$.$ If the annual inflation rate during the year is $2\mathrm{.}50$ percent, calculate the principal amount

used to determine the first coupon payment and the first coupon payment $($paid on June

$30,2020).$

b$.$ Calculate the inflation$-$adjusted principal at the end of the second six months $($on

December $31,2020)$ and the coupon payment to the investor for the second six$-$month

period. What is the inflation$-$adjusted principal on this coupon payment date?

c$.$ What is the total coupon payment over the year?