Unit 5: Basic Long-Term Financial Concepts

Lesson 5.2
Effective Annual Interest Rate
Contents
Introduction 1

Learning Objectives 2

Quick Look 3

Learn the Basics 4

Effective Annual Interest Rate 4
Importance of Effective Annual Interest Rate 5
The Effects of Compounding Periods 5
Steps in Calculating the Effective Annual Interest Rate 7

Keep in Mind 9

Try This 10

Practice Your Skills 11

Challenge Yourself 12

Photo Credit 13

Bibliography 13
Unit 5: Basic Long-Term Financial Concepts

Lesson 5.2

Effective Annual Interest Rate

Introduction

It is the nature of Filipinos to grab opportunities where they could save on expenses. People
tend to buy more if there is a shop-wide sale. Online shopping sites use different strategies
to attract customers, such as lowering the prices on holidays or special occasions, offering
free delivery, and other freebies. Physical stores also use the "Buy 1, Take 1" scheme to
dispose of perishable or outdated goods. Naturally, people are more drawn to these
promotional activities because of their desire to save more.

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Unit 5: Basic Long-Term Financial Concepts

Similarly, banks and other financial institutions offer attractive interest rates to draw
individuals to borrow from them. Do you know how to compute the actual amount of
money you need to pay when presented with interest rates? How will you know if you are
actually capable of paying off debts on time? In this lesson, you will learn the importance of
computing the annual interest rate.

Learning Objectives DepEd Competency

Compute for the effective annual interest rate

In this lesson, you should be able to do the
(ABM_BF12-IIIg-h-18).
following:
● Describe effective annual interest rate.

● Perform the steps in computing an

effective annual interest rate.
● Compute for the effective annual interest
rate.
● Explain the importance of an effective
annual interest rate.

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Unit 5: Basic Long-Term Financial Concepts

Quick Look

Money Lending
Some Filipinos, due to heavy financial problems, would avail of illegal money lending
schemes with risky and disadvantageous terms. Because of their urgent need for financial
relief and inadequate information about other effective means of sourcing funds, they enter
into agreements with suspicious people and entities. Loans obtained from such activities
would usually have ridiculously high interest rates.

However, some individuals approach banks, credit card companies, and other legitimate
financial institutions when they are in need of additional funds. With regards to the interest
rate that should be imposed by the lending companies, there are currently no ceilings set
for the imposition of interest rates, in view of Central Bank Circular No. 905, series of 1982,
which suspended the effectiveness of the Usury Law. As such, the borrower and lender are
free to agree on the interest rates, fees, and other charges that will apply to the loan in their
agreement.

Questions to Ponder
1. Why do some Filipinos resort to illegal sources when borrowing funds?
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2. Is it better to have credit cards in case of emergencies?

________________________________________________________________________________________
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3. What do you think is the proper use of credit cards?

________________________________________________________________________________________
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Unit 5: Basic Long-Term Financial Concepts

Learn the Basics

Investing is a serious decision that involves risks—risks1 that you would not want to sacrifice
out of impulsive decisions. On the other hand, borrowings2 are a profound way of acquiring
funds. Mishandling loans would sink the ship at once. These two activities—investing and
financing—are the two main problems that the company must address adequately.

Essential Question

How do we identify which lending companies offer lower interest?

Effective Annual Interest Rate

Effective annual rate (EAR) is an interest that determines the actual return on an
investment or the precise amount of interest due on a credit or loan. It is an interest rate
adjusted for compounding3 over a given period.

EAR is commonly used to compare different loans and investments with annual interest rates
and different compounding periods. In other words, EAR can be used to assess interest
payable on debt or earnings from an investment. The formula for EAR is:

where:
EAR = Effective Annual Rate
i = annual interest rate
n = number of compounding periods

1
Risk (noun) - the degree of uncertainty and/or potential financial loss inherent in an investment decision.
2
Borrowings (noun) - obtains some form of loan. Interest is used in almost all loans and financial borrowing.
3
Compounding (noun) - generating earnings from previous earnings.

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Unit 5: Basic Long-Term Financial Concepts

Importance of Effective Annual Interest Rate

The effective annual interest rate is a strategic tool that reveals the accurate return on an
investment or loan interest rate. The principle in EAR is that the higher the compounding
period, the higher the actual interest.

Without the help of EAR, borrowers might be deceived into underestimating the actual cost
of a loan. As a result of the misleading, an individual may experience more financial
problems such as paying off debts on time. For the interested investors, EAR helps them
project the actual expected return on investment. It allows them to make sound decisions
about investing their hard-earned money.

Closer Look

Differentiating Interests
Mr. Cruz decided to purchase high-tech equipment that his business
needs. Since he does not have enough cash to finance the new
equipment, he decided to look for financial institutions that offer
business loans.

He learned that both Bank ABC and Bank DEF offer a loan with 7%
interest. At first, he thought that he could just choose from any of the two
bank offers. However, upon examining the terms further, he learned that
Bank ABC’s loan interest will compound quarterly, while Bank DEF will
compound monthly.

Mr. Cruz decided to take up Bank ABC’s offer since its Effective Annual
Interest is less compared to Bank DEF’s.

The Effects of Compounding Periods

The interest rate has two forms: (1) the nominal rate, which does not take into account the
compounding period and is also known as the annual percentage rate (APR), and (2) the
effective rate, which considers the compounding period and gives more accurate interest
charges.

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Unit 5: Basic Long-Term Financial Concepts

Figure 1. Borrowers and investors should examine the nominal and effective interest rates.

APR is commonly used for banks, credit card companies, and other business transactions. It
is a great way to lure clients by presenting attractive rates- lower interest rate for debt and
higher interest return for investment. However, the use of EAR will give a more accurate
process of how interest will affect maintaining credit or holding an investment. Table 1
illustrates the comparison of APR and EAR for four different compounding periods:

Table 1. Comparison of APR and EAR for four different Compounding Periods

EAR EAR EAR EAR

APR
Semi-Annually Quarterly Monthly Daily

10% 10.25% 10.38% 10.47% 10.51%

15% 15.56% 15.85% 15.07% 16.17%

20% 21.00% 21.55% 21.93% 22.13%

25% 26.56% 27.44% 29.07% 28.39%

The APR of 10% is actually 10.25% if it is compounded semi-annually, 10.38% if compounded

quarterly, 10.47% if compounded monthly, and 10.51% if compounded daily. The idea of EAR
gives an accurate interest of charge or return. The more often the compounding period
occurs, the higher the effective interest rate.

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Unit 5: Basic Long-Term Financial Concepts

Check Your Progress

If investment A has an annual interest of 5% compounded monthly and

investment B has an annual interest of 5% compounded semi-annually,
which investment is better?
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Steps in Calculating the Effective Annual Interest Rate

To calculate the effective annual interest rate with the use of the formula, follow the steps
below:

Step 1: Determine the stated interest rate. The APR or the nominal rate is the stated
interest rate usually found as the clickbait or the headlines of the loan or deposit.

Step 2: Identify the compounding period. Basically, the compounding periods are monthly
or quarterly.
Table 2. Compounding Periods

Compounding
Number of Periods
Frequency

Annually 1

Semi-Annually 2

Quarterly 4

Monthly 12

Bi-Weekly 26

Weekly 52

Daily 365

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Unit 5: Basic Long-Term Financial Concepts

Step 3: Apply the EAR formula.

𝑖 𝑛
𝐸𝐴𝑅 = (1 + 𝑛
) − 1

Closer Look

Calculating the EAR

A credit company charges 12% interest per year compounded monthly.
What effective annual rate does the company charge?

Step 1: Determine the stated interest rate.

𝑖 = 0. 12
Step 2: Identify the compounding period.
𝑛 = 12
Step 3: Apply the EAR formula.
𝑖 𝑛
𝐸𝐴𝑅 = (1 + 𝑛
) − 1

0.12 12
𝐸𝐴𝑅 = (1 + 12
) − 1
12
𝐸𝐴𝑅 = (1 + 0. 01) − 1
𝐸𝐴𝑅 = 1. 12682 − 1
𝐸𝐴𝑅 = 0. 12682
𝐸𝐴𝑅 = 12. 68%

Check Your Progress

If you are an investor, would you prefer an investment with interest that has
more compounding periods or those with less (provided that the stated
interest are the same)? Explain your answer.
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Unit 5: Basic Long-Term Financial Concepts

Keep in Mind

● Effective annual rate (EAR) is an interest that determines the actual return on an
investment or the precise amount of interest due on a credit or loan.
● Banks and financial institutions present interest rates in two forms: nominal rate and
the effective rate. The former does not consider the compounding period, while the
latter does. If you want to know the actual return or interest due, you must compute
the effective rate.

● The formula for calculating EAR is:

where:
EAR = Effective Annual Rate
i = annual interest rate
n = number of compounding periods

● In general, more frequent compounding periods result in higher effective annual

interest rates. A lower EAR is preferable when making loans debts while higher EAR
when making investments.

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Unit 5: Basic Long-Term Financial Concepts

Try This

A. Identification. Write the correct answer on the provided space before each number.

________________ 1. It is used to determine the exact rate of return in an investment

or interest charged in a loan.

________________ 2. An interest that does not take compounding periods into

account.

________________ 3. The number of periods when compounded monthly.

________________ 4. A higher EAR is preferable in this activity.

________________ 5. A lower EAR is preferable in this activity.

B. True or False. Write true if the statement is correct. Otherwise, write false.

________________ 1. EAR is always higher than APR unless the interest is only
compounded annually.

________________ 2. More often compounding periods mean higher interest.

________________ 3. EAR can only be used for investing purposes only.

________________ 4. Banks and other financial institutions use APR to lure

customers.

________________ 5. EAR includes compounding periods into account.

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Unit 5: Basic Long-Term Financial Concepts

Practice Your Skills

Effective Annual Rate

1. An investor gathered information regarding each company's interest rate return. He

asked for your help to determine which company has a bigger return on investment.
Complete the table by supplying the effective annual interest rate in each column.

Effective Annual
Company Annual Interest Rate
Rate

Company A 17% compounded semi-annually

Company B 17% compounded annually

Company C 17% compounded quarterly

Company D 17% compounded monthly

2. In which company should the investor invest his money? Explain your answer.
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3. A businessman would like to get a loan from a bank to renovate his store. He
gathered information regarding each bank's interest rate. Help the businessman
decide in which bank he should get his loan. Complete the table by supplying the
effective annual interest rate in each column.

Effective Annual
Company Annual Interest Rate
Rate

Bank A 5% compounded quarterly

Bank B 5% compounded monthly

Bank C 5% compounded semi-annually

Bank D 5% compounded annually

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Unit 5: Basic Long-Term Financial Concepts

4. In which bank should the businessman get his loan? Explain your answer.
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5. Why each bank do not use the EAR instead of the APR?
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___________________________________________________________________________________________

Challenge Yourself

Answer the following questions:

1. Company A charges 12% interest on loans compounded semi-annually, and
Company B charges 12% interest on loans compounded monthly. Which company
has a better deal? Explain your answer.
_________________________________________________________________________________________
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_________________________________________________________________________________________
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2. A businessman decided to invest his money in a company. Company X offers 15%

interest compounded monthly, while Company Y offers 15% compounded quarterly.
In which company should the businessman invest his money? Explain your answer.
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________

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Unit 5: Basic Long-Term Financial Concepts

3. Provide a scenario wherein failure to compute the Effective Annual Interest can
cause drastic effects on a business’s performance. Explain your answer.
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Photo Credit
Shopping Venture by Preis King is licensed under Pixabay License via Pixabay.

Bibliography
“Effective Annual Interest Rate.” Corporate Finance Institute, January 22, 2022.
https://corporatefinanceinstitute.com/resources/knowledge/finance/effective-annua
l-interest-rate-ear/.

Fernando, Jason. “What the Effective Annual Interest Rate Tells Us.” Investopedia.
Investopedia, August 19, 2021.
https://www.investopedia.com/terms/e/effectiveinterest.asp#:~:text=What%20Is%2
0an%20Effective%20Annual,card%2C%20or%20any%20other%20debt.

Gitman, Lawrence and Chad Zutter. Principles of Managerial Finance, 14th Edition. Harlow:
Pearson Education Limited, 2015.

GOVPH. “Frequently Asked Questions.” Securities and Exchange Commission. Accessed

January 22, 2022.
https://www.sec.gov.ph/lending-companies-and-financing-companies-2/frequently-a
sked-questions/#:~:text=Are%20%E2%80%9C5%2D6%E2%80%9D%20

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transactions,subject%20to%20the%20court's%20determination.

Nolan, Paul. “What Is Effective Annual Interest Rate?” The Balance. The Balance, August 4,
2021. https://www.thebalance.com/what-is-effective-annual-interest-rate-5092472.

Nominal and effective interest. Accessed January 22, 2022.

https://global.oup.com/us/companion.websites/9780190296902/sr/interactive/form
ulas/nominal/#top.

5.2. Effective Annual Interest Rate 14