Independent solution

How to solve this Coupon Rate Interpolation question

Setup

Setup

Represent coupon rate r as x/F + y, where F is redemption value. The first two bonds provide two linear equations for x and y.

r=x/F+yr=x/F+y

Model

Model

Solving those equations gives x = 96.8 and y = −0.044. Insert the third redemption value 1,320 into the same relationship.

0.0528=x/1000+y,0.0440=x/1100+y0.0528=x/1000+y,\quad0.0440=x/1100+y

Compute

Compute

The third coupon rate is 96.8/1,320 − 0.044 = 0.02933, or 2.93%.

x=96.8, y=−0.044,r3=96.8/1320−0.044=0.02933x=96.8,\ y=-0.044,\quad r_3=96.8/1320-0.044=0.02933

Answer

Answer

The calculation gives 2.93% for coupon rate interpolation, matching published choice B.

r=2.93%(B)\boxed{r=2.93\%\quad\text{(B)}}