Provide explanation or calculation tosupport your answer. $1.$Inflation$-$indexed Treasury bonds are intended for investors who wish to ensure that the returns on their investments keep up with the increase in interest rate over time. A ten$-$year, inflation$-$indexed bond has a par value of $$10,000$ and a coupon rate of $5$ percent. During the first six months since the bond was issued, the inflation rate was $2$ percent. Based on this information, the coupon payment after six months will be $$250.$

a$.$ Trueb. False