Math
posted by Sarah .
How long will it take for an investment to double in value if it earns 9.5% compounded continuously?

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