Independent solution

How to solve this Perpetuities with Different Frequencies question

Setup

Setup

Use the first perpetuity price to recover its effective annual yield. Because payments are every two years, its geometric ratio is based on the two-year accumulation factor.

7.21=1+1(1+i)2−1⟹i=0.07757.21=1+\frac1{(1+i)^2-1}\Longrightarrow i=0.0775

Model

Model

The second perpetuity has a different payment interval and yield. Discount its first payment to time 0 and value the remaining three-year-spaced payments as a geometric perpetuity.

7.21=R(1.0875)−1(1+1(1.0875)3−1)7.21=R(1.0875)^{-1}\left(1+\frac1{(1.0875)^3-1}\right)

Compute

Compute

Substitution of the recovered rate in the second pricing equation gives R = 1.74.

R=1.74R=1.74

Answer

Answer

The calculation gives 1.74 for perpetuities with different frequencies, matching published choice D.

R=1.74(D)\boxed{R=1.74\quad\text{(D)}}