Hi, so I have the steps for deducing the present value of annuity from the formula for the sum of the geometric series. However, I don't seem to understand step a,b and c. I know how to deduce the present value of annuity, but not in this way.
Asked
Active
Viewed 740 times
1 Answers
0
It's just horrid notation. They use some symbols twice with different meanings. If you add new symbols, the confusion disappears: what happens is that they have a formula for a geometric sum which is
$$S_n=\frac{a(1-x^n)}{1-x} \; .$$
And they now that $A$ is expressed as a geometric sum, so identifying the ratio $x$ and the first term $a$:
$$a = R(1+r)^{-1}$$
and
$$x=(1+r)^{-1} \; ,$$
they can conclude that
$$A = \frac{R(1+r)^{-1}(1-(1+r)^{-n})}{1-(1+r)^{-1}} \; .$$
The rest is just algebraic manipulations until the end result.
Raskolnikov
- 16,108