Suppose that the annual coupon rate for a TIPS is 2%. Suppose further that an investor purchases $100,000 of par value (initial principal) of this issue today and that the semiannual inflation rate is 1.25% (so the annual inflation rate is 2.5%). What is the dollar coupon interest that will be paid in cash at the end of the first six months?

$1012.50 ( dollar coupon interest paid at the end of  6 months  )

Explanation:

par value ( initial value ) of TIPS = $100000 ( PO)

coupon rate = 2% ( r )

Annual inflation rate = 2.5% ( R )

semi-annual inflation rate = 1.25%

A) what is the dollar coupon interest paid after 6 months

=  inflation adjusted principal after 6 months *  r / 2   equation 1

inflation adjusted principal after 6 months( P1 ) = PO * ( 1 + R /2 ) equation 2

                                         = 100000 * ( 1 + 1.25% ) = 100000 * 1.0125=$101250

therefore back to equation 1

P1 * 0.02 / 2 = 101250 * 0.01 = $1012.50 ( dollar coupon interest paid after 6 months  )