alishakarmali
alishakarmali alishakarmali
  • 08-06-2017
  • Mathematics
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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?

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jdoe0001 jdoe0001
  • 08-06-2017
[tex]\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \qquad \qquad \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 6.5\%\to \frac{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+\frac{0.065}{365} \right)^{365}\implies 0.06715284876964462628 \\\\\\ \textit{which rounds up to }\approx 0.0672\qquad 0.0672\cdot 100\approx 6.72\%[/tex]
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