Question

Find the annual percentage yield​ (APY) in the following situation. A bank offers an APR of 4.4​% compounded daily. The annual percentage yield is (blank) %

Answer 1

$\bf ~~~~~~ \textit{Annual Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.4\%\to \frac{4.4}{100}\dotfill &0.044\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily then 365} \end{array}\dotfill &365 \end{cases} \\\\\\ \left(1+\frac{0.044}{365}\right)^{365}-1~~ \approx 0.0449796\implies \stackrel{\textit{rounded up}}{0.045}\implies \stackrel{\textit{to percent}~\hfill }{0.045\cdot 100\implies 4.5}$

Answer 2

Step-by-step answer:

APY (annual percentage yield) is the amount of interest in percent one would actually earn by investing a sum of money in a year.

It takes into account the interest rate expressed in any particular form, and the compounding period.

In the current market, most interest rates (for example, credit cards) are expressed in APR (Annual percentage rate) which is an underestimate of the actual amount to be paid, by NOT taking into account the compounding period, monthly (instead of annually) most of the time.  The shorter compounding period increases the APY.

Here the APR is 4.4%.  to take into account the compounding period, we divide the interest rate by 12 to give the monthly rate, 4.4%/12=0.044/12.

This rate will then be compounded 12 times to give the APY, or the future value after 12 months.

Future value = (1+0.044/12)^12 = 1.044898

Therefore the APY is 1.044898 less initial deposit, or

1.044898-1 = 0.044898, or 4.4898%, or 4.49% (rounded to 2 decimal places)