Geometric Progression

Study guide: Exam FM-2

In the context of annuities, a geometric progression refers to a sequence of payments where each payment is a constant multiple (1+g) of the previous one. Starting from 1, the payments are 1, (1+g), (1+g)^2, \ldots

• This is the basis of the Geometric Increasing Annuity.
• The present value for n payments (annuity-immediate):

\text{PV} = \frac{1}{1+i} \cdot \frac{1-\left(\frac{1+g}{1+i}\right)^n}{1 - \frac{1+g}{1+i}}

= \frac{1-(1+g)^n(1+i)^{-n}}{i-g}

i \neq g

• For a geometric Perpetuity (i > g): \text{PV} = 1/(i-g).

Geometric Perpetuity A cash flow starts at 5{,}000 at end of year 1 and grows at 2\% per year forever. Find the PV at i=8\%.

Answer \text{PV} = \frac{5000}{0.08 - 0.02} = \frac{5000}{0.06} = 83{,}333