Question

What is the effective annual rate on an investment that pays interest of 6.5% continuously? The answer is 6.72%. How do we get to this?

Answer 1

`\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \qquad \qquad \left(1+(r)/(n)\right)^(n)-1 \\\\ \begin{cases} r=rate\to 6.5\%\to (6.5)/(100)\to &0.065\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{continuously, 365 days, thus} \end{array}\to &365 \end{cases} \\\\\\ \left(1+(0.065)/(365) \right)^(365)\implies 0.06715284876964462628 \\\\\\ \textit{which rounds up to }\approx 0.0672\qquad 0.0672\cdot 100\approx 6.72\%`