Consider an account with an APR of 8.5%. Find the APY with daily compounding.
(1 + .085/365)^365 = 1.0887
or, 8.87%
To find the APY (annual percentage yield) with daily compounding, you can use the formula:
APY = (1 + (APR/n))^n - 1
Where:
APR = Annual percentage rate (in decimal form)
n = Number of compounding periods in one year
In this case, the APR is 8.5% and it is compounded daily, so n = 365 (number of days in a year).
Let's calculate the APY:
APY = (1 + (0.085/365))^365 - 1
Now, let's solve this equation step by step using a calculator:
1. First, divide 0.085 by 365:
0.085 / 365 = 0.00023287671
2. Add 1 to the result from step 1:
1 + 0.00023287671 = 1.00023287671
3. Raise the result from step 2 to the power of 365:
(1.00023287671)^365 = 1.08621918451
4. Subtract 1 from the result from step 3 to get the APY:
1.08621918451 - 1 = 0.08621918451
So, the APY with daily compounding for an account with an APR of 8.5% is approximately 8.62%.
To find the Annual Percentage Yield (APY) with daily compounding, you can use the following formula:
APY = (1 + r/n)^n - 1
Where:
- r represents the annual interest rate (expressed as a decimal)
- n represents the number of compounding periods per year
In this case, the APR (Annual Percentage Rate) is given as 8.5%, so r = 0.085.
Since the interest is compounded daily, there are 365 compounding periods in a year, so n = 365.
Now let's substitute these values into the formula:
APY = (1 + 0.085/365)^365 - 1
Using a calculator or a spreadsheet, evaluate the expression to get the APY:
APY ≈ 0.08757, or approximately 8.757%
Therefore, the Annual Percentage Yield (APY) with daily compounding for an account with an APR of 8.5% is approximately 8.757%.