Question

How long will it take money to double if it is invested at 9% compounded quarterly? 7.7% compounded continuously?

Answer 1

\[2x=x(1+.09/4)^{4t}\]\[2=(1.0225)^{4t}\]\[\log_{10}2=\log_{10}(1.0225)^{4t} \]\[\log_{10}2=4t \log_{10}(1.0225) \]\[\log_{10}2/\log_{10}(1.0225)=4t \]
t=7.78 years

Continuously at 7.7%

\[2x=x(e ^{.077t})\]\[2=e ^{.077t}\]\[\ln 2=\ln e ^{.077t}\]\[\ln 2=.077t\]\[\ln 2/.077=t\]
t=9 years

Answer 2

Thank you so much!!!