A.CRE

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.

Frequently Asked Questions about Annual Percentage Yield (APY)

APY is the true rate of return earned on an investment or paid on a loan, accounting for compounding interest. It’s also known as the Annual Effective Rate.

The formula is:
APY = (1 + APR / n)ⁿ – 1,
where APR is the annual percentage rate and n is the number of compounding periods per year.

APR is a nominal interest rate assuming simple interest with no compounding. APY reflects the real return or cost after accounting for compounding, and is therefore always equal to or higher than APR.

APY is often used to express the net return expected by investors—such as equity return rates—giving a more accurate view of investment performance over time.

The more frequently interest is compounded, the higher the APY will be compared to the APR. For example, quarterly compounding increases the APY more than annual compounding.

With a $15 million loan at 4.5% APR compounded quarterly (n = 4), the APY is approximately 4.59%, calculated using:
(1 + 0.045/4)^4 – 1

You can explore glossary entries on APY, Annual Effective Rate, and Annual Percentage Rate, or review Case Study #11 – Residential Development Business Model: Build And Sell for applied examples.

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