Question

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

Answer 1

A)

$\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3.1196\%\to \frac{3.1196}{100}\to &0.031196\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2 \end{cases} \\\\\\ \left. \qquad \qquad\right. \left(1+\frac{0.031196}{2}\right)^{2}-1$

b)

$\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3.1184\%\to \frac{3.1184}{100}\to &0.031184\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4 \end{cases} \\\\\\ \left. \qquad \qquad\right. \left(1+\frac{0.031184}{4}\right)^{4}-1$

c)

$\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3.1095\%\to \frac{3.1095}{100}\to &0.031095\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, assuming 365 days} \end{array}\to &365 \end{cases} \\\\\\ \left. \qquad \qquad\right. \left(1+\frac{0.031095}{365}\right)^{365}-1$

d)

$\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3.1172\%\to \frac{3.1172}{100}\to &0.031172\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve times} \end{array}\to &12 \end{cases} \\\\\\ \left. \qquad \qquad\right. \left(1+\frac{0.031172}{12}\right)^{12}-1$

Answer 2

i just took the apex quiz its 3.1172%