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

Question

anonymous · Answer

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):$$t=\dfrac{\ln 2}{.07}\approx 10 \text{ years}$$

riley · Answer

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

anonymous · Answer

Glad to help! :-)