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