Question 65473
{{{V[T] = P(1 - r)^T}}}
{{{V[T]}}} is the value after T years
P is the purchase price
r is the annual interest rate
T is number of years after the 3 month trial period
Note that {{{T >= 0}}} and {{{T = 0}}} is when the 
3 month trial period has ended
{{{T}}}(years) = ({{{t}}}(months) - 3) / 12
Note that when {{{t = 3}}}, T = 0 and {{{V(T) = P(1 - r)^T = P}}}
as it should.
When {{{t = 15}}}, {{{T = 1}}} (1 year after trial)
and V(1) = {{{830(.87)}}}
V(1) = {{{722.10}}} 
What is the value after 1 year? I assume this means 1 year after
purchase, not 1 year after the 3 month trial.
Set {{{t = 12}}} then {{{T = (12 - 3) / 12}}}
{{{T = 9 / 12}}}
{{{T = 3/4}}}
V(3/4) = {{{ 830(1 - .13)^(3/4)}}}
V(3/4) = {{{830(.87)^(3/4)}}}
V(3/4) = {{{830 * .900}}}
V(3/4) = {{{747.68}}}
So, the value after a year is $ 747.68