Time Value of Money: How to Calculate the Effective Annual Rate (EAR)

In order to be smart and calculative in personal finance matters, understanding the time value of money is an essential part of the learning process. I will be posting a series of computation methods related to time value of money on every Wednesday.

Today, we will learn to calculate the actual effective annual rate (EAR).

Common Problems

If you have deposit money in a Fixed Deposit (FD) account, most like you was asked about the term of your deposit – 1 month, 3 months, 6 months, 1 year or longer? The bank gives different rate for different tenure. Let’s say Maybank is giving 3.7% for 12 months FD, and 3.4% for 6 months FD, what is the EAR for 6-months FD? Is it better than 12-months FD?

Theory

Scenario 1 – 12-month FD
Referring to the situation above, let’s say you are depositing RM10,000 in FD for 12 months tenure. At the end of the term, you will get your initial investment (RM10k) plus the 3.7% interest (RM370)

Return = 3.7% p.a. , which is also the EAR.

Scenario 2 – 6-month FD

If you opt to put the money in 6-months FD, after 6 months, you will get

Return = 3.4% x (6/12) = 1.7% , which is equal to RM170 interest earned.

Then you renew the FD without withdrawing the interest earning, you will have RM10,170 in the FD for another 6 months.
At the end of the year, your will get another earning of 1.7% x RM10,170 = RM172.89.

So your total return is RM170+RM172.89 = RM342.89

The Effective Annual Rate (EAR) = RM342.89/RM10,000 = 3.4289%

To easily calculate the EAR, use the formula below:

where i = nominal annual rate (normally stated);
n = number of compounding period (compounding frequency);

For the above example

EAR = [(1+ 0.034/2)^2] – 1
      = 3.4289%

Nominal Interest Rate

Photo by wmjas

Nominal interest rate is what we usually see on financial products. Most of the time, these rates may not be the actual annual rate.
An interest rate is called nominal if the frequency of compounding (e.g. a month) is not identical to the basic time unit (normally a year).

Example:

• interest rate on housing loan (EAR is higher when it is daily rest)
• published FD rates for different terms (1 month, 2 months, or 12 months etc)

The more frequent you compound, the higher the EAR.

When you want to compare plans, first you must calculate the respective EAR for each plan. Then compare the EAR.

Use this EAR convertor

Exercise

You have RM7,000 in Fixed Deposit with CIMB Bank. Your FD is renewable every month and CIMB bank provides 3.2%p.a. interest. You let the FD renewed for 2 years. From the 3rd year onwards, the bank lowered the FD interest rate to 3.0% p.a. But you don’t need the money, so you leave it there for another 3 years. What’s the final amount you will be able to withdraw at the end of 5 years?

Post your answer in the comment section. The first commenter who posted the right answers will get a special 3D birthday card sponsored by Pigeon Card.

Previous Tutorial on Time Value of Money

How to calculate the value of single sum investment {Time Value of Money Tutorial}
Finding the Rate of Return to Meet Financial Goals {Time Value of Money Tutorial}
Computing the Value of a Fixed Sum Invested Regularly {Time Value of Money Tutorial}
How to Calculate the total money in EPF Account