compare the annual percentage yield for three banks. Bank 1 offers an APR of 3.8% compounded daily; bank 2 offers an APR of 4.1% compounded monthly; bank 3 offers an APR of 4.5% compounded quarterly
3.8% compounded daily ---> (1+.038/365)^365 = 1.038729
4.1% compounded monthly --> (1 + .041/12)^12 = 1.041779
4.5% compounded quarterly --> (1 + .045/4)^4 = 1.045765
Find the annual percentage yield (APY) in the following situation.
A bank offers an APR of 3.8% compounded daily.
To compare the annual percentage yield (APY) for three banks, you need to understand how compound interest works. Compound interest is when interest is calculated not only on the initial deposit but also on any accumulated interest.
To calculate the APY, you need to use the formula:
APY = (1 + (APR / n))^n - 1
Where:
- APR: Annual Percentage Rate
- n: Number of compounding periods per year
Now let's calculate the APY for the three banks:
Bank 1:
APR: 3.8%
Compounded daily implies there are 365 compounding periods per year (since there are 365 days in a year).
Using the formula, we can calculate the APY for Bank 1:
APY1 = (1 + (0.038 / 365))^365 - 1
Bank 2:
APR: 4.1%
Compounded monthly implies there are 12 compounding periods per year.
Using the formula, we can calculate the APY for Bank 2:
APY2 = (1 + (0.041 / 12))^12 - 1
Bank 3:
APR: 4.5%
Compounded quarterly implies there are 4 compounding periods per year.
Using the formula, we can calculate the APY for Bank 3:
APY3 = (1 + (0.045 / 4))^4 - 1
Now, you can calculate the APY for each bank by substituting the values into the respective formulas. This will give you the annual percentage yield for each bank.