Posted by **Sarah** on Sunday, November 21, 2010 at 8:09pm.

How long will it take for an investment to double in value if it earns 9.5% compounded continuously?

- Math -
**MathMate**, Sunday, November 21, 2010 at 10:43pm
For r=0.095, with normal compound interest, compounded yearly, the number of years to double at a rate of r% is ln(2)/ln(1+r)=ln(2)/ln(1.095)=7.638 years.

from A=P(1+r)^n

take ln both sides,

ln(A/P)=n ln(1+r)

n=ln(2)/ln(1+r)

With continuous compounding,

A=Pe^{rn}

Take logs

ln(A/P)=e^{rn}

ln(2)=rn

n=ln(2)/r

=ln(2)/0.095

=7.296 years

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