Question

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

4.0784% compounded monthly
4.0798% compounded semiannually
4.0730% compounded daily

Answer 1

Option C is correct.

Explanation:

The formula is =
`(1+(r)/(n))^(n)-1`

r = rate of interest

n = number of times its compounded

1. 4.0784% compounded monthly

here n = 12

`(1+(0.040784)/(12))^(12) -1` = 1.0403-1 = 0.0403

2. 4.0798% compounded semiannually

here n = 2

`(1+(0.040798)/(12))^(2) -1` = 1.0066-1 = 0.0066

3. 4.0730% compounded daily

here n = 365

`(1+(0.040730)/(12))^(365)` = 3.328-1 = 2.328

Answer 2

`\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ ~~~~~~~~~~~~\textit{4.0784\% compounded monthly}\\\\ ~~~~~~~~~~~~\left(1+(r)/(n)\right)^(n)-1 \\\\ \begin{cases} r=rate\to 4.0784\%\to (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+(0.040784)/(12)\right)^(12)-1\\\\ -------------------------------\\\\ ~~~~~~~~~~~~\textit{4.0798\% compounded semiannually}\\\\`


`\bf ~~~~~~~~~~~~\left(1+(r)/(n)\right)^(n)-1 \\\\ \begin{cases} r=rate\to 4.0798\%\to (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+(0.040798)/(2)\right)^(2)-1\\\\ -------------------------------\\\\`


`\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\ ~~~~~~~~~~~~\left(1+(r)/(n)\right)^(n)-1 \\\\ \begin{cases} r=rate\to 4.0730\%\to (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+(0.040730)/(365)\right)^(365)-1`