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%.