"Dave Dodson" <> wrote in message

news: ups.com...

> Let's define some symbols: P0 = the initial principal in the fixed

> account ($10,000 in your example), A = the initial amount withdrawn

> ($500), r = the rate of increase of the withdrawal (5%), and n = the

> number of years. Then we need to solve the equation

>

> A * ((1+r)^n - 1) / r = P0.
Yes, but where did that come from? - solving it is the easy part :-).

The withdrawal at the end of year 1 is $500

The withdrawal at the end of year 2 is $500 * (1 + 5%)

The withdrawal at the end of year 3 is $500 * (1 + 5%) ^ 2, ...

The total withdrawals are $500 * [1 + (1 + 5%)^1 + (1+5%)^2 + ... +

(1 + 5%)^(n-1) ]

or algebraically, A * [ 1 + (1+r)^1 + (1+r)^2 + ... + (1+r)^(n-1)]

Using the formula for the value of a finite geometric series

http://mathworld.wolfram.com/GeometricSeries.html
we get the expression on the left hand side.

> Thus, n = int(log(P0*r/A + 1) / log(1+r))

>

> Here, int() is the greatest integer function, and log is the base-10

> logarithm.
Log can be any base - base 10, base e, base 2, it doesn't matter.

As this is misc.invest.financial-plan, where would such a situation arise,

where a drawing account were effectively kept under a pillow (i.e. in a

non-interest bearing account)? I can't see that happening in a trust

(fiduciary duty to invest prudently), but I suppose it might happen in some

business accounts?

--

Mark Freeland