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Annual Percentage Rate vs. Annual Percentage Yield

Annual Percentage Rate vs. Annual Percentage Yield!
Do You Know the Difference? Does It Matter Anyway?

In this blogpost, I help you understand and interpret the Stated Returns / Stated Rate of Interest linked to various popular financial products such as Bank FDs, Home Loans and MF SIP Products.

In this regard, I bring to you the difference between two very important terms that find a lot of relevance in personal financial planning; The Annual Percentage Rate (Hereafter referred to as APR) and the Annual Percentage Yield (Hereafter referred to as APY), also known as the Effective Annual Rate (EAR)

Let’s first quickly understand what these two terms mean:

Annual Percentage Rate (APR):
APR indicates the Annual Returns / Annual Rate of Interest (linked to investment products, savings products and loan products) without accounting for compounding frequency.

Annual Percentage Yield (APY) / Effective Annual Rate (EAR):
APY indicates the Annual Returns / Annual Rate of Interest (linked to investment products, savings products and loan products) after adjusting for compounding frequency.

Note: In cases where the compounding frequency is 1, both APR and APY are equal.

Why is it Important to know these terms?

Knowing these terms is important in helping us understand the stated returns on financial products like Bank FDs, the historical / indicative performance of MF SIPs, the applicable interest rates on loans, etc. Understanding them closely will help us assess their real implications on our planning and on our overall finances.

Let’s understand them closely with the help of appropriate illustrations:

Here’s what the Stated Annual Interest Rate on a Home Loan tells you:

When a Bank offers a 7.5% p.a. Rate of Interest on a Home Loan, the Effective Annual Rate (EAR) or APY at which the borrower pays back the Bank is slightly higher than the stated rate i.e. the borrower ends up paying an Effective Annual Rate (EAR) or APY of 7.76% p.a. approx. This is because the borrower pays the loan back in monthly installments, thereby implying an Annual Compounding Frequency of 12, which isn’t accounted for in the Stated Rate of Interest. Adjusting for this compounding effect is what leads us to an APY of 7.76% p.a. approx.

How do we interpret the Stated Annual Rate of Interest, offered by a Bank FD?

A Bank FD promising a fixed return of 6% p.a. actually ends up offering an annual yield of 6.14% p.a. approx. This is because the annual rate on offer in the case of Bank FDs is usually expressed as APR i.e. a rate that doesn’t take the compounding frequency into consideration. In the case of Bank FDs, compounding happens 4 times a year. Thus, with an Annual Compounding Frequency of 4, the Effective Annual Rate (EAR) or APY earned after factoring in the impact of compounding turns out to be slightly higher than the stated rate.

Thus in this case,
• The Stated Annual Rate of Interest = 6% p.a. (APR)
• The Effective Annual Rate of Interest Earned = 6.14% p.a. approx. (APY)


Now let’s compare this with a Monthly MF SIP product:

In the case of an MF SIP, the stated historical performance figures or the indicative future performance figures, unlike Bank FDs, are usually stated after accounting for compounding frequency i.e. in terms of Effective Annual Rate (EAR) or APY. So for instance, a 12% p.a. historical / indicative returns on a Monthly SIP product tells you what you effectively stand to gain per year after adjusting for compounding.

Thus in this case,
Stated historical returns / indicative future returns = 12% p.a. (APY)

However, if one were to use these figures to plan a Monthly SIP to achieve a targeted corpus, the APY figures will have to be converted to APR for precise results.

APR <- -> APY Conversion Using EXCEL:

Here I introduce to you two simple yet important EXCEL functions that can help you with APR <- -> APY conversion.

Convert any APR figure into APY using the EFFECT Function in EXCEL.

Here’s the formula:

where,
• EFFECT is the required output in APY (Output).
• nominal_rate is the Stated Rate of Interest / Historical or Indicative Returns (Input)
• npery is the number of compounding periods in a year (Input)

Now consider a Bank FD with a Stated Rate of Interest of 6% p.a. and an Annual Compounding Frequency of 4. Upon substituting the Input fields with the relevant figures, we get an APY of 6.14% p.a. approx.

Similarly, for a Home Loan offered by a Bank at a Stated Interest Rate of 7.5% p.a. and an Annual Compounding Frequency of 12, the same formula can be applied by the borrower to compute the effective annual outgo in terms of APY. Upon substituting the input fields with the relevant figures, we get an APY of 7.76% p.a. approx.

Convert any APY figure into APR using the NOMINAL Function in EXCEL.

Here’s the formula:

=NOMINAL (effect_rate, npery)

where,
NOMINAL is the required output in APR (Output)
effect_rate is the Effective Annual Rate of Interest or APY (Input)
npery is the number of compounding periods in a year (Input)

The question that arises here is why would one need the APR when the returns are stated clearly in APY terms.
Let’s take an example here to understand:
For an MF SIP product, the returns, whether historical or indicative, are stated in APY terms. However, when it comes to planning a Monthly SIP to achieve a target corpus, based on these historical or indicative figures, one will have to convert the APY into APR before proceeding with the other relevant EXCEL functions. This is because the payments happen monthly and therefore the impact of compounding needs to be factored in. Thus for a Monthly MF SIP Product with a historical / indicative future returns of 12% p.a. (APY), and an Annual Compounding Frequency of 12, substituting the inputs fields in the formula with the relevant figures will give us an APR of 11.39% p.a. approx. The APR, thus computed, can be used alongside other relevant TVM functions to compute the Monthly Payments required.

Conclusion:

On the face of it, the difference between APR and APY appears to marginal. However, when seen over a reasonably long time horizon, the variance becomes too substantial to be overlooked. Thus for a Tech Savvy New Age Do-It-Yourself (D.I.Y.) Investor, understanding such terms and their implications, will go a long way in helping them create financial plans that offer a less distorted view of the future.

Note: In this post, I have touched upon a very small but critical aspect related to the interpretation of returns and how it affects your financial plans. I will keep writing on several such topics in the times to come. Till then stay connected.
 

About the author


Deepak Rameshan, CERTIFIED FINANCIAL PLANNERCM, Dip TD, MMS.
Deepak Rameshan is a CFPCM professional, and has been working in the financial services domain for close to 13 years. He holds a Master’s Degree in Management Studies and a Diploma in Training & Development and has been actively engaged in Training & Content Development during this period. As a Personal Finance Enthusiast and an avid researcher of the subject, Deepak has delivered several Investor Awareness Workshops over the years covering areas such as Risk Planning & Insurance, Retirement & Goal planning, Tax Planning and a few other specialized areas. He takes keen interest in writing and has penned numerous articles for this blog, addressing some of the most relevant concerns that individuals face with respect to their finances.
“Financial Planning Standards Board Ltd. (FPSB Ltd.) is the proprietor of the CFPCM, CERTIFIED FINANCIAL PLANNERCM and marks outside the United States, including in India, and permits qualified individuals to use these marks to indicate that they have met FPSB Ltd.’s initial and ongoing certification requirements.”
Watch this space for more insights on Personal Finance…
Watch this space for more insights on Personal Finance
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