Independent solution

How to solve this Perpetuities at Different Frequencies question

Setup

Setup

Let v be the annual discount factor. The first perpetuity pays every three years, so its geometric ratio is v³.

32=10v31−v3⟹v3=324232=\frac{10v^3}{1-v^3}\Longrightarrow v^3=\frac{32}{42}

Model

Model

Its quoted value gives 32 = 10v³/(1 − v³), hence v³ = 32/42. The second stream’s payment interval is obtained by taking the corresponding root of v before applying the perpetuity formula.

X=v1/31−v1/3X=\frac{v^{1/3}}{1-v^{1/3}}

Compute

Compute

Substitution in q/(1 − q) gives 32.599. The requested value is 32.6.

X=32.599X=32.599

Answer

Answer

The calculation gives 32.6 for perpetuities at different frequencies, matching published choice B.

X=32.6(B)\boxed{X=32.6\quad\text{(B)}}