Question

3P(0)=P(0)e^15%*t

i need to find the time(years) it takes for that amount of money to triple if compounded continuously at a rate of 15%

Answer 1

P is the principal and the amt is 3P annual rate of interest is 15%
let t be the no of yrs
then we have
3P=P(1+.15)^t
3=(1+.15)^t
or 3= 1.15^t
taking log to the base 10 both sides we hav

log 3= t * log 1.15
or t = log 3 / log 1.15

Answer 2

t=0.4771/.06 =7.951 = appx 8 yrs

Answer 3

The formula for continuous compounding is as follows:
\[A=Pe ^{rt}\]
where A is the amount after t years, P is the principal and r is the annual interest rate expressed as a decimal.
e is the exponential number.
Using the formula in your question, but expressing the interest rate as a decimal we get
\[3P _{0}=P _{0}e ^{0.15t}\ ............(1)\]
Simplifying equation (1) gives
\[3=e ^{0.15t}\ .................(2)\]
Taking natural logs of both sides of equation (2) we get
\[\ln 3=0.15t\ ...............(3)\]
and we find the time t from
\[t=\frac{\ln 3}{0.15}=7.324\ years\]