brandinbradfor brandinbradfor
  • 27-11-2017
  • Mathematics
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An investment declines in value by 3% each month. By what percentage does its value decline in a year ?

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jdoe0001 jdoe0001
  • 27-11-2017
[tex]\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12 \end{cases} \\\\\\ \left(1+\frac{0.03}{12}\right)^{12}-1\implies 1.0025^{12}-1~~\approx ~~ 0.03041596 \\\\\\ r\%=0.03041596\cdot 100\implies r\approx\stackrel{\%}{3.04}[/tex]
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