Title: What is Annual Percentage Yield (APY) — a clear, practical guide
Definition
– APY (Annual Percentage Yield) is the annualized return on an account or investment that includes the effect of compounding interest. In plain terms: APY tells you the real percentage growth you will earn over one year if the balance and compounding pattern remain unchanged.
Why APY matters
– Stated interest rates (the nominal rate) don’t tell the full story when compounding occurs at different intervals (daily, monthly, quarterly, etc.). APY standardizes those differences so you can compare products on an apples-to-apples basis.
– A higher APY is better for depositors because it means more growth; however, APY does not include account fees or penalties, so check those separately.
Key formulas
– APY (annualized, from nominal rate and compounding frequency):
APY = (1 + r/n)^n − 1
where r = nominal annual interest rate (decimal), n = number of compounding periods per year.
– Future value with compounding (useful to convert APY into dollar outcomes):
X = D × (1 + r/n)^(n × y)
where X = final amount, D = initial deposit, y = number of years.
Definitions of terms
– Nominal rate: the stated annual interest rate before compounding.
– Compounding period: how often interest is credited (daily, monthly, quarterly, etc.).
– Compound interest: interest paid on both the original principal and accumulated interest.
Step-by-step: how to compute APY
1. Convert the stated percentage to a decimal (e.g., 6% → 0.06).
2. Divide that decimal by n (compounding periods per year).
3. Add 1 to the result.
4. Raise that sum to the n power.
5. Subtract 1 to get APY in decimal form; convert to percent by multiplying by 100.
Worked numeric examples