Independent solution

How to solve this Annuities and Perpetuities question

Setup

Setup

Use six months as one payment and interest period.

23=a¨∞∣ j=1+1j23=\ddot a_{\infty|\,j}=1+\frac{1}{j}

Model

Model

The first unit is paid immediately, so the stream is a perpetuity-due.

j=122j=\frac{1}{22}

Compute

Compute

Its value determines the half-year rate; two such factors produce the annual effective rate.

i=(1+j)2−1=0.092975i=(1+j)^2-1=0.092975

Answer

Answer

The annual effective rate is approximately 9.3%, corresponding to choice E.

i≈9.3%(E)\boxed{i\approx9.3\%\quad\text{(E)}}