Question

Susan plans to invest $400 at 15% annual interest compounded continuously. When will her investment triple in value?

Answer 1

If the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by:

$A=P\cdot e^{rt},$

P: the principal, amount invested

A: the new balance

t: the time

r: the rate, (in decimal form).

So,

$1200=400\cdot e^{0.15\cdot t},\\ e^{0.15\cdot t}=3,\\ t=\cfrac{\text {ln }3}{0.15}=7.324\text{ years}\approx7\text{ years }4\text{ months.}$