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oee [108]
3 years ago
10

The savings account offering which of these APRs and compounding periods offers the best APY?

Mathematics
2 answers:
zzz [600]3 years ago
7 0
\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}\\\\


\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\\\\
-------------------------------\\\\


\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
Paladinen [302]3 years ago
7 0

Answer:

Option C is correct.

Step-by-step explanation:

The formula is = (1+\frac{r}{n})^{n}-1

r = rate of interest

n = number of times its compounded

1. 4.0784% compounded monthly

here n = 12

(1+\frac{0.040784}{12})^{12} -1 = 1.0403-1 = 0.0403

2. 4.0798% compounded semiannually

here n = 2

(1+\frac{0.040798}{12})^{2} -1 = 1.0066-1 = 0.0066

3. 4.0730% compounded daily

here n = 365

(1+\frac{0.040730}{12})^{365} = 3.328-1 = 2.328

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