Final answer:
To find the APY with quarterly compounding, divide the APR by the number of compounding periods per year (4 for quarterly). Use the formula APY = (1 + i)^n - 1, where i is the interest rate per compounding period and n is the number of compounding periods per year. For monthly compounding, the APY is 4.836%. For daily compounding, the APY is 4.953%.
Step-by-step explanation:
To find the APY with quarterly compounding, we first calculate the interest rate per compounding period. To do this, we divide the annual interest rate (APR) by the number of compounding periods per year. In this case, since we have quarterly compounding, there are 4 compounding periods per year. So, the interest rate per compounding period is 4.7% / 4 = 1.175%.
To find the APY, we use the formula:
APY = (1 + i)^n - 1
Where i is the interest rate per compounding period and n is the number of compounding periods per year. For quarterly compounding, n = 4.
Plugging in the values, we get:
APY = (1 + 0.01175)^4 - 1
= (1.01175)^4 - 1
= 1.04874 - 1
= 0.04874 (or 4.874%)
So, the APY with quarterly compounding is 4.874%.
For monthly compounding, the interest rate per compounding period is 4.7% / 12 = 0.3917%. Using the same formula and plugging in the values, we get an APY of 4.836%.
For daily compounding, the interest rate per compounding period is 4.7% / 365 = 0.0129%. Again, using the formula, we find an APY of 4.953%.