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Complete the information requested for each of the following $1,000 face value, zero-coupon bonds, assuming semiannual...

Complete the information requested for each of the following $1,000 face value, zero-coupon bonds, assuming semiannual compounding. Do not round intermediate calculations. Round your answers for maturity and yield to two decimal places and round your answer for price to the nearest cent.

Bonds Maturity (Years) Yield (%) Price ($)

A

16 10%
B 8% $595
C 10 $395
0 0
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Answer #1

Bond A:

Face Value = $1,000

Annual YTM = 10.00%
Semiannual YTM = 5.00%

Time to Maturity = 16 years
Semiannual Period = 32

Current Price = $1,000 / 1.05^32
Current Price = $209.87

Bond B:

Face Value = $1,000
Current Price = $595

Annual YTM = 8.00%
Semiannual YTM = 4.00%

Let Semiannual Period be n

$595 = $1,000 / 1.04^n
1.04^n = 1.6806723
n * ln(1.04) = ln(1.6806723)
n = 13.24

Semiannual Period = 13.24

Time to Maturity = 2 * 13.24
Time to Maturity = 26.48 years

Bond C:

Face Value = $1,000
Current Price = $395

Time to Maturity = 10 years
Semiannual Period = 20

Let Semiannual YTM be i%

$395 = $1,000 / (1 + i)^20
(1 + i)^20 = 2.531646
1 + i = 1.0475
i = 0.0475 or 4.75%

Semiannual YTM = 4.75%

Annual YTM = 2 * 4.75%
Annual YTM = 9.50%

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