In: Finance
The ask yield on a 6 percent coupon Treasury bond maturing in eight years is 5.488 percent. If the face value is $1,000, what should be the QUOTED cost of the bond today (use semiannual compounding)?
A. 103.2795
B. 107.2542
C. 106.8542
D. 108.5511
E. 104.3678
Par value | $1,000.00 | ||||
Coupon Interest rate = |
6% | ||||
Semiannual coupon rate |
3% | ||||
Interest per coupon |
(1000*3%) = |
$30.00 | |||
YTM rate | 5.488% | ||||
Semiannual YTM rate = |
2.744% | ||||
No. of years |
8 | ||||
No. of periods (10 Years * 2) |
16 | ||||
Calculation of price of bond @ 2.744% YTM |
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Annual Interest received = |
30.00 | ||||
Cumulative P.V.F. @ 2.744 % for 16 periods = |
|||||
(1- ((1/(1.02744)^16)))/0.02744 |
12.81050102 | ||||
Present value of interest received (30 * 12.81050) |
$384.32 | ||||
Maturity amount received = |
1000 | ||||
P.V.F. @ 2.744 % for 16 th period = |
0.648479852 | ||||
(1/(1+0.02744)^16) |
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Present value of Maturity amount(1000*0.648479) |
$648.48 | ||||
Price of bond |
$1,032.79 | ||||
Quoted price of bond = 1032.79/1000 * 100 = |
103.2794883 | ||||
So, Quoted price of bond is 103.2795%. Answer A. |
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