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In December 2018, the U
In December 2018, the U.S. Treasury issued 30-year bonds with a coupon rate of 3.1%, paid semiannually. The principal will be repaid in December 2048, and the bond's face value is $1000, paying coupons every six months until maturity. The market interest rate was 2.5% in December 2018 and you intended to hold the bond until maturity, what would have been the fair price for this bond by the time of its issuance? (choose the most accurate answer) .
A) $996
B) $1,126
C) $1,316
D) $1,526
E) Other
Expert Solution
Computation of the price of the bond:-
Price of bond = (Annuity*((1-1/(1+rate)^n)/rate)) + (FV/(1+rate)^n)
Here,
Coupon payment = $1,000*3.1%/2 = $15.50
Rate = 2.5%/2 = 1.25% (semiannual)
n = 30*2 = 60 periods (semiannual)
Price of bond = ($15.50*((1-1/(1+1.25%)^60)/1.25%)) + ($1,000/(1+1.25%)^60)
= ($15.50*42.03459) + ($1,000/2.10718)
= $651.54 + $474.57
= $1,126.10 Or $1,126
Hence, the correct option is B) $1,126
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