Investments

All rates are expressed as annual rates in this question.  A floating-rate bond pays LIBOR + 50 basis points semi-annually, has a face value of $1,000 and matures in 5 years’ time.  The coupon rate of the bond has just been set based on the market 6-month LIBOR rate of 2%.  

Suppose you buy the bond today and in 3 months’ time the 3-month LIBOR rate is 2.50%, the 6-month LIBOR rate is 2.75% and the market perception of the issuer’s credit quality has changed such that similar bonds issued now would require them to pay only 30 basis points above LIBOR.  What is the price of the bond at this 3-month mark (show all workings carefully)?