You are considering a 15-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 8.05%, how much should you be willing to pay for the bond? Do not round intermediate steps. Round your answer to the nearest cent.
face value = | 1000 |
Years remaining to Maturity = | 15 |
Semiannual periods (n)= (15*2) = | 30 |
Coupon rate = | 8.00% |
Semiannual Coupon = 1000*8%/2 = | 40 |
Required annual effective rate = | 8.05% |
EAR = ((1+semiannual rate)^no of compounding in year)-1 |
|
8.05% =( (1+i)^2)-1 |
|
1+0.0805 = (1+i)^2 |
|
1+i= (1.0805)^(1/2)= | 1.039471019 |
i= | 0.03947101932 |
so Semiannual yield = | 0.03947101932 |
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n |
|
40*(1-(1/(1+0.03947101932)^30))/0.03947101932 + 1000/(1+0.039471019)^30 |
|
1009.206189 | |
So we will be willing to pay for bond $1,009.21 |
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You are considering a 15-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. If you r...
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