Independent solution

How to solve this Duration and Convexity question

Setup

Setup

Because the annual coupon rate is twice yield, the annual coupon is 4,000 times the yield.

3609.29=4000[1−(1+i)−30]+2250(1+i)−303609.29=4000\left[1-(1+i)^{-30}\right]+2250(1+i)^{-30}

Model

Model

Substitute that relation into the bond price formula to isolate the maturity discount factor.

(1+i)−30=4000−3609.294000−2250=0.223263(1+i)^{-30}=\frac{4000-3609.29}{4000-2250}=0.223263

Compute

Compute

The implied yield is 5.1251%; convert the stated Macaulay duration by dividing by one plus yield.

i=0.051251,Dmod=14.411.051251=13.7075i=0.051251,\qquad D_{\mathrm{mod}}=\frac{14.41}{1.051251}=13.7075

Answer

Answer

The modified duration is 13.71 years, corresponding to choice C.

Dmod≈13.71 years(C)\boxed{D_{\mathrm{mod}}\approx13.71\text{ years}\quad\text{(C)}}