Independent solution

How to solve this Geometric Perpetuity Due question

Setup

Setup

Work in quarters and let vq be the quarterly discount factor. The perpetuity-due begins immediately, and successive payments grow by 0.5%.

100000=20001−1.005vq100000=\frac{2000}{1-1.005v_q}

Model

Model

Its present value is a geometric series with ratio 1.005vq. Setting the value to 100,000 gives vq = 0.98/1.005.

vq=0.98/1.005v_q=0.98/1.005

Compute

Compute

Convert the quarterly discount factor to an annual effective rate: vq to the power −4 minus 1 equals 0.10601, or 10.6%.

i=vq−4−1=0.10601i=v_q^{-4}-1=0.10601

Answer

Answer

The calculation gives 10.6% for geometric perpetuity due, matching published choice D.

i=10.6%(D)\boxed{i=10.6\%\quad\text{(D)}}