$50.00 after 0 months and $37.50 after 6 months.
We first must calculate half-life using the attached formula.
Half-Life = (time * ln(2)) / ln (beginning amount/ending amount)
Half-Life = (6 * 0.69314718056) / ln (50.00 / 37.50)
Half-Life = (
<span>
<span>
<span>
4.1588830834
</span>
</span>
</span>
) / ln (
<span>
<span>
<span>
1.3333333333
</span>
</span>
</span>
)
Half-Life = (
<span>
<span>
4.1588830834
</span>
</span>
) / 0.28768207245
Half-Life =
<span>
<span>
<span>
14.456525038
</span>
</span>
</span>
months
Now we need to calculate "lambda"
lambda = ln(2) / half-life
lambda = 0.69314718056 / <span>14.456525038
lambda = </span><span><span><span>0.0479470121
</span>
</span>
</span>
Next we have to use this formula:
Ending Amount = beginning amount • e^( -lambda • time )
(where "e" is the mathematical constant 2.718281828...)
Ending Amount = 50 * 2.718281828^<span>(-0.0479470121*24 months)
</span><span>Ending Amount = 50 * 2.718281828^(-1.1507282904)
</span>Ending Amount = 50 *
<span>
<span>
<span>
0.3164062499
</span>
</span>
</span>
Ending Amount =
<span>
<span>
<span>
15.82</span></span></span> dollars
**********************************************************************
As a DOUBLE-CHECK we can work this out every 6 months:
0 months $50
6 months = $50 - (50 *.25) = 37.50
12 months = $37.50 -(37.50 *.25) = <span>28.125
18 months = $28.125 -(28.125 * .25) = 21.09375 </span>
24 months = $21.09375 -(21.09375 * .25) =
<span>
<span>
<span>
15.8203125
</span>
</span>
</span>
You'll find this page quite helpful:
http://www.1728.org/halflif2.htm
