A 10,000 par value bond with coupons at 8%, convertible semiannually, is being sold

$9,124.94

Explanation:

the clean price of the bond two months ago was $5,640.

Currently, interest rate have changed and the price of the bond has changed:

the semiannual yield is 4%, that means that the bimonthly yield = 1.04 = (1 + r)³

1 + r = 1.0132

r = 0.0132

the current price of the bond:

PV of face value = $10,000 / (1 + 0.0132)²⁰ = $7,693.01

PV of coupon payments = ($300 x {[1 - (1 + 0.04)⁻⁶] / 0.04}) / (1 + 0.0132)² = $1,572.64 / (1 + 0.0132)² = $1,531.93

minus accrued interests (dirty price) = $300 x 1/3 = $100

Market value of bond = $9,124.94

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