Annual Percentage Yield

Annual Percentage Yield (APY) is the true rate of return earned taking into account compounding interest. Also known as the Annual Effective Rate, the formula for APY is as follows:

• • APY = ( 1 + APR / n ) ^ n – 1
  • Periodic Rate = ( 1 + APY ) ^ ( 1 / n ) – 1
  • n = Frequency of compounding within a year

APY is used in the context of net returns expected by investors: i.e. equity return rate.

For any given annual percentage rate, the corresponding annual percentage yield will always be a little higher depending on how many times it is compounded within the year.

Putting Annual Percentage Yield (APY) in Context

Imagine an investor group that acquires a multi-family residential complex for $15 million. To finance this investment, they obtain a mortgage with an Annual Percentage Rate (APR) of 4.5%. The interest on this loan compounds quarterly. In this scenario, understanding the APY is crucial for accurately assessing the actual cost of the loan over time.

• • Loan Amount: $15,000,000
  • APR: 4.5%
  • Compounding Frequency (n): 4 (quarterly)

Using the APY formula:

• • APY = (1 + APR/n)^n – 1 = (1 + 0.045/4)^4 – 1
  • APY: ≈ 4.59%

The APY of 4.59% indicates the true cost of the loan considering the effects of compounding interest quarterly. This rate is slightly higher than the nominal APR of 4.5%, illustrating how the frequency of compounding elevates the effective interest rate.

This detailed calculation allows the investor group to better understand the annual financial burden imposed by their financing choice, providing a clearer picture than APR alone. This metric is essential for investors aiming to compare investment opportunities accurately and manage their portfolios efficiently.