Question

How long, to the nearest year, will it take an investment to double if it is continuously compounded at 7% per year?

Answer 1

Recall the following formula for continuously compounding interest:\[P(t)=P_0e^{rt}\]Since we want our value to double the initial investment, we must find the value of t that satisfies the following:\[2P_0=P_0e^{rt}\]\[e^{rt}=2\]\[rt=\ln 2\]\[t=\dfrac{\ln 2}{r}\]Plug in the known value of r and evaluate using a calculator, rounding to the nearest whole number (year):\[t=\dfrac{\ln 2}{.07}\approx 10 \text{ years}\]

Answer 2

ty so much yakeyglee, I completely understand how you did that, and see what I was doing wrong. ty again!!

Answer 3

Glad to help! :-)