A Treasury bond was bought and sold for $102.200 and $101.050 respectively.The accumulated value of all coupons was $18.If the bond was held for exactly four years and the bond paid coupons semi-annually, then the realised yield-to-maturity on this bond was:

Question

Quizplus · Accepted Answer

Using the bond pricing formula, we can solve for the yield-to-maturity:

$102.200 = \frac{\$18}{(1+\frac{y}{2})^8} + \frac{\$100}{(1+\frac{y}{2})^8}$
$101.050 = \frac{\$18}{(1+\frac{y}{2})^8} + \frac{\$100}{(1+\frac{y}{2})^8}$

Simplifying and solving for y, we get:

$y = 7.70\%$

However, this yield is the annual yield, not the semi-annual yield that we are looking for. To convert to the semi-annual yield, we divide by 2 to get:

$y_{SA} = 3.85\%$

Therefore, the realized yield-to-maturity on this bond was 3.85% p.a.

A Treasury Bond Was Bought and Sold for $102