Question 33003
e = 2.71828.
Seems familiar? Its the same as our rate.
{{{ A  =   P(e)^Yr}}}
That is our final formula.<P>
So we get,
P=10,000
R=2.7183
Years=Y
A=20,000
Continuous compounding:
{{{ A  =   P(e)^Yr}}}
{{{ 20000=10000(e)^Yr}}}
{{{ 2 = (e)^Yr}}}
So log of 2 to the base 'e' is equal to 'Yr'
Log to the base e is also called natural logarithm,or ln()
{{{ Ln(2) = Yr }}}
{{{ Ln(2) = Y(2.7183) }}}
{{{ (Ln(2))/2.7183 = Y }}}
Now to convert log to ln we need to multiply by 2.303
{{{ Y = (Ln(2))/2.7183 }}}
{{{ Y = 2.303*Log(2)/2.7183 }}}
{{{ Y = 0.8472*Log(2) }}}
{{{ Y = 0.8472*0.3010 }}} (from log tables)
Y=0.255
Obviously,this is a bit small,so adjusting the decimal values we get:
Y=25.5
<P>
So to double your money at continous compound rate 'e',
you'd need 25.5 years.
<P>
Hope this helps,
xC