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A zero coupon bond matures in eight years. It is sold to yield 5% annually. Find the modified duration D(.05,1)

This question comes from the Second Edition Mathematics Interest Theory textbook, section 9.2 #3. The answer provided is D(.05,1)= 7.61905 I am unsure how to approach the problem given that there are no prices or coupon amounts given. Any help in the right direction would be great, thanks!

uytt
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  • You can express it as a function of Price and Face, or make an assumption. many textbooks have an automatic "implied" price and face when they are not specified in the problem. – Joe Feb 07 '18 at 21:01
  • @uytt Why don't you do accept the answers? – alexjo Feb 08 '18 at 10:52
  • I'm sorry I am new to the website, how do I accept the answer? I appreciate your help! @alexjo – uytt Feb 08 '18 at 17:47

1 Answers1

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The Macaulay duration is $$ D(0.05,\infty)=8 $$ and, observing that $D(i,\infty)=(1+i)D(i,1)$, the modified duration is $$ D(0.05,1)=\frac{8}{1.05}\approx 7.61905 $$

alexjo
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