
Explanation:
The correct answer is A ($0.57). The value of a bond is calculated using the present value formula:
PV = [PMT / (1 + r)^1] + [PMT / (1 + r)^2] + ... + [(PMT + FV) / (1 + r)^N]
PV = [PMT / (1 + r)^1] + [PMT / (1 + r)^2] + ... + [(PMT + FV) / (1 + r)^N]
where:
Calculation Steps:
$2.5, FV = $100, PV = $108), the yield is 1.114% semiannually (2.228% annually).$2.5, FV = $100, and r = 0.614%, the new price is $107.43.$108.00 - $107.43 = $0.57.Why Not B or C?
$1.52) incorrectly fails to annualize the interest rate before computing the change.$3.08) incorrectly uses the same time to maturity without adjusting for the passage of one year.A three-year, semiannual-pay bond with a 100 par value and a 5% coupon rate is purchased for 108. One year later, if the yield to maturity has decreased by 100 basis points, the change in the bond's value is closest to:
A
$0.57.
B
$1.52.
C
$3.08.
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