Respuesta :
[tex]\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
~~~~~~~~~~~~\textit{4.0784\% compounded monthly}\\\\
~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0784\%\to \frac{4.0784}{100}\to &0.040784\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{monthly, thus twelve}
\end{array}\to &12
\end{cases}
\\\\\\
\left(1+\frac{0.040784}{12}\right)^{12}-1\\\\
-------------------------------\\\\
~~~~~~~~~~~~\textit{4.0798\% compounded semiannually}\\\\
[/tex]
[tex]\bf ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0798\%\to \frac{4.0798}{100}\to &0.040798\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2 \end{cases} \\\\\\ \left(1+\frac{0.040798}{2}\right)^{2}-1\\\\ -------------------------------\\\\ [/tex]
[tex]\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\ ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0730\%\to \frac{4.0730}{100}\to &0.040730\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\to &365 \end{cases} \\\\\\ \left(1+\frac{0.040730}{365}\right)^{365}-1[/tex]
[tex]\bf ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0798\%\to \frac{4.0798}{100}\to &0.040798\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2 \end{cases} \\\\\\ \left(1+\frac{0.040798}{2}\right)^{2}-1\\\\ -------------------------------\\\\ [/tex]
[tex]\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\ ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0730\%\to \frac{4.0730}{100}\to &0.040730\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\to &365 \end{cases} \\\\\\ \left(1+\frac{0.040730}{365}\right)^{365}-1[/tex]
Answer:
Option C is correct.
Step-by-step explanation:
The formula is = [tex](1+\frac{r}{n})^{n}-1[/tex]
r = rate of interest
n = number of times its compounded
1. 4.0784% compounded monthly
here n = 12
[tex](1+\frac{0.040784}{12})^{12} -1[/tex] = 1.0403-1 = 0.0403
2. 4.0798% compounded semiannually
here n = 2
[tex](1+\frac{0.040798}{12})^{2} -1[/tex] = 1.0066-1 = 0.0066
3. 4.0730% compounded daily
here n = 365
[tex](1+\frac{0.040730}{12})^{365}[/tex] = 3.328-1 = 2.328
