What is the current price of this zero coupon bond

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A 30-year bond is maturing in 5 years. The par value is \$1000. The coupon rate is 6%. Coupon payment is made semi-annually. The price of this bond is \$950. a) What is the yield to maturity? b) A new-issued 5-year zero coupon bond has the same yield spread as the 30-year bond. What is the current price of this zero coupon bond if the par value is \$1000. c) Because of a power outage in the exchange, the liquidity premium is increased by 0.5%. What is the price of the 30-year bond now?

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