Question

In: Finance

The ask yield on a 6 percent coupon Treasury bond maturing in eight years is 5.488...

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

Solutions

Expert Solution

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

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)

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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