# 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:

$Effective Annual Rate formula$

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?

## Previous Tutorial on Time Value of Money

#### KCLau

personal finance author and trainer

• nik siong

• KCLau

Hi Nik Siong,

Congratulations!

• mllclim

\$7,000.00 3.2% 01.01.07 \$18.6667
\$7,018.67 3.2% 01.02.07 \$18.7164
\$7,037.38 3.2% 01.03.07 \$18.7664
\$7,056.15 3.2% 01.04.07 \$18.8164
\$7,074.97 3.2% 01.05.07 \$18.8666
\$7,093.83 3.2% 01.06.07 \$18.9169
\$7,112.75 3.2% 01.07.07 \$18.9673
\$7,131.72 3.2% 01.08.07 \$19.0179
\$7,150.73 3.2% 01.09.07 \$19.0686
\$7,169.80 3.2% 01.10.07 \$19.1195
\$7,188.92 3.2% 01.11.07 \$19.1705
\$7,208.09 3.2% 01.12.07 \$19.2216
\$7,227.31 3.2% 01.01.08 \$19.2728
\$7,246.59 3.2% 01.02.08 \$19.3242
\$7,265.91 3.2% 01.03.08 \$19.3758
\$7,285.29 3.2% 01.04.08 \$19.4274
\$7,304.71 3.2% 01.05.08 \$19.4792
\$7,324.19 3.2% 01.06.08 \$19.5312
\$7,343.73 3.2% 01.07.08 \$19.5833
\$7,363.31 3.2% 01.08.08 \$19.6355
\$7,382.94 3.2% 01.09.08 \$19.6879
\$7,402.63 3.2% 01.10.08 \$19.7404
\$7,422.37 3.2% 01.11.08 \$19.7930
\$7,442.17 3.2% 01.12.08 \$19.8458

\$7,462.01 3.0% Yr 2009 \$223.8603
\$7,685.87 3.0% Yr 2010 \$230.5761
\$7,916.45 3.0% Yr 2011 \$237.4934

\$8,153.94 Total

i didnt get the answer right. May i know where did i go wrong? Thank you.

• KCLau

@mllclim,

the last three years should be compounded monthly too, just like what you’ve done for the first 2 years.

• kelvin

Mr KC Lau,
can you show me how to calculate ROI And EAR.
If I purcahse a saving plan for 20 yrs cost me Rm 20,000 and my returned at them is only Rm18,000. what is my ROI and EAR.
what happen if i don’t surrender and 10 yrs later i withdraw and the amount are Rm40,000
what is my ROI and EAR?
please ahow me in detail how to calculate for the above 2 scnerio.
i am very weak in math and hopefully you can show me more in detail.
tks.

• meg

3.2% compounded monthly = 3.247% p.a. (using the above formula)
3.0% compounded monthly = 3.0416% p.a.

1st year: 7000*3.247% = 7227.315 (rounding error)
2nd year: 7227.315*3.247% = 7462.011
3rd year: 7462.011*3.0416% = 7688.975
4th year: 7688.975*3.0416% = 7922.843
5th year: 7922.843*3.0416% = 8163.824

• Carol

Hi KC Lau, in your example above, what is the ear per annum for the five-year period and how is it calculated? TIA!

• chea F. Kennedy

Calculating EAR You are looking at an investment that has an effective annual
rate of 16 percent. What is the effective semiannual return? The effective quarterly
return? The effective monthly return?

• AnTakTau

the formula partially correct.

you should include inflation rate. last figure that i known, it stand at 3.0++%.

all in all, your fixed deposit only growing by numbers, not the real value.

Mr KC Lau,
can you show me how to calculate this exercise Using annual, semiannual, and quarterly compounding periods for each of the following, (1) calculate the future value if \$5,000 is deposited initially, and (2) determine the effective annual rate (EAR).
a. At 12% annual interest for 5 years.
b. At 16% annual interest for 6 years.
c. At 20% annual interest for 10 years.

• KCLau