You find the following Treasury bond quotes. To calculate the number of years un

Question

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2016. The bonds have a par value of $1,000.

In the above table, find the Treasury bond that matures in May 2038. What is the asked price of this bond in dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Asked price            $

If the bid-ask spread for this bond is .0644, what is the bid price in dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Bid price            $

Rate Maturity
Mo/Yr Bid Asked Chg Ask
Yld ?? May 23 103.5423 103.5301 +.3261 5.939 6.102 May 28 104.4913 104.6370 +.4257 ?? 6.148 May 38 ?? ?? +.5366 3.971

Explanation / Answer

1.

Face value = $1,000

Coupon rate = 6.148%

Semi-annual coupon amount = $1,000 * 6.148% * ½ = $30.74

Years to maturity = May 2016 to May 2038 = 22 years

Semi-annual periods to maturity (n) = 22 years * 2 = 44

Yield on the bonds = 3.971%

Semi-annual yield (r) = 3.971%/2 = 1.9855% = 0.019855

Price of bond = Present value of remaining coupon payments + Present value of face value

Present value of annuity = Annuity*{1-(1+r)-n}/r

Present value of annuity of remaining 44 coupon payments = $30.74*(1-1.019855-44)/0.019855 = $30.74*29.1601 = $896.38

Present value of face value = $1,000/1.01985544 = $1,000/2.3751 = $421.03

Price of bond = $896.38+$421.03 = $1,317.41

Ask price of bond = $1,371.41

2.

Bid ask spread = 0.0644

Bid price = $1,371.41 - $0.0644 = $1,317.35

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