# find the annual percentage yield (to the nearest 0.01%). a bank offers an APR of 3.1% compounded daily.

## let the equivalent annual rate be i

daily rate = .031/365 = .000084931

1.000084931^365 = 1+i

1+i = 1.031484143

i = annual = .03148

annual rate = .03148 or appr 3.15%

Scott's answer would be the **instantaneous** rate at .0314855

which of course would be very close to the daily compounded rate

## thank you

## To find the annual percentage yield (APY), we can use the following formula:

APY = (1 + r/n)^n - 1

Where:

r is the annual interest rate (APR) in decimal form

n is the number of compounding periods in a year

In this case, the bank offers an APR of 3.1% and interest is compounded daily, so we have:

r = 0.031 (3.1% in decimal form)

n = 365 (since interest is compounded daily)

Substituting these values into the formula, we get:

APY = (1 + 0.031/365)^365 - 1

Calculating this expression, we find that the APY is approximately 3.14% to the nearest 0.01%.