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Answer: $99.03
A bond paying 2.0% annually with semiannual coupons pays $1 every six months, plus $100 principal at maturity. Discount each cash flow using the given continuously compounded spot rates: \[ 1\cdot e^{-0.01\cdot 0.5} + 1\cdot e^{-0.016\cdot 1.0} + 1\cdot e^{-0.019\cdot 1.5} + 101\cdot e^{-0.025\cdot 2.0} \] This equals **$99.03**. So the correct answer is **B**.
Author: Manit Arora
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Question 158.2. Bond price using spot rates
Assume the following continuously compounded zero rates: 1.0% at 0.5 years; 1.6% at 1.0 year; 1.9% at 1.5 years; and 2.5% at 2.0 years. What is the theoretical price of a bond with a $100 principal that pays coupons at the rate of 2.0% semiannually?
A
$98.03
B
$99.03
C
$100.03
D
$101.03
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