Independent solution

How to solve this Macaulay Price Approximation question

Setup

Setup

Let i be today's annual effective yield and i minus 0.005 the new yield. Convert modified duration to Macaulay duration by multiplying by one plus i.

DMac,k=Dmod,k(1+i)D_{\mathrm{Mac},k}=D_{\mathrm{mod},k}(1+i)

Model

Model

Use Bond 1 to solve the Macaulay approximation equation for the otherwise unknown current yield.

21,635.83=20,400(1+i1+i−0.005)11.735(1+i)21{,}635.83=20{,}400\left(\frac{1+i}{1+i-0.005}\right)^{11.735(1+i)}

Compute

Compute

The numerical solution is i = 0.04488408. Apply the same rate ratio with Bond 2's duration.

X=20,400(1.044884081.03988408)13.101(1.04488408)X=20{,}400\left(\frac{1.04488408}{1.03988408}\right)^{13.101(1.04488408)}
X=21,784.466X=21{,}784.466

Answer

Answer

The approximated Bond 2 value is 21784.47, choice E.

X≈21,784.47(E)\boxed{X\approx21{,}784.47\quad\text{(E)}}