Introduction: Why Interest Rate Terminology Matters
When opening a savings account, investing in certificates of deposit (CDs), or applying for a mortgage, you will encounter terms like APR (Annual Percentage Rate), Compound Interest, and APY (Annual Percentage Yield). While they sound similar, small mathematical differences between them can result in thousands of dollars over time.
What Is Simple Interest vs. Compound Interest?
Simple Interest is calculated solely on the original principal sum. If you invest $1,000 at 5% simple interest per year, you earn $50 every year regardless of how long the money stays in the account.
Compound Interest calculates interest on both the initial principal and the accumulated interest from previous periods. In year one, $1,000 earns $50. In year two, you earn 5% on $1,050 ($52.50), causing your wealth to grow exponentially.
The Compound Interest Formula
The standard compound interest formula is:
- A: Final balance (Principal + Total Interest)
- P: Initial Principal amount
- r: Annual nominal interest rate (expressed as a decimal)
- n: Number of compounding periods per year (e.g. 12 for monthly, 365 for daily)
- t: Time in years
What Is APY (Annual Percentage Yield)?
APY is the effective annual rate of return after accounting for compounding. It standardizes different compounding frequencies into a single annualized rate, making it easy to compare financial accounts.
The Impact of Compounding Frequency
Consider $10,000 invested at a 6% nominal rate (r = 0.06) over one year under different compounding schedules:
- Annual (n=1): A = 10,000 × (1 + 0.06)^1 = $10,600.00 (APY = 6.00%)
- Quarterly (n=4): A = 10,000 × (1 + 0.015)^4 = $10,613.64 (APY = 6.136%)
- Monthly (n=12): A = 10,000 × (1 + 0.005)^12 = $10,616.78 (APY = 6.168%)
- Daily (n=365): A = 10,000 × (1 + 0.06/365)^365 = $10,618.31 (APY = 6.183%)
The more frequently interest compounds, the higher the APY and final returns.