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
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?
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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
nik siong January 2, 2008 at 10:55 pm
the answer is RM 8163.82.
KCLau January 17, 2008 at 11:30 am
Hi Nik Siong,
You’ve got the right answer!
Congratulations!
mllclim January 31, 2008 at 11:34 am
$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 February 2, 2008 at 11:23 am
@mllclim,
the last three years should be compounded monthly too, just like what you’ve done for the first 2 years.
kelvin April 18, 2009 at 10:45 pm
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 December 10, 2009 at 2:10 pm
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 January 19, 2010 at 12:51 pm
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 October 20, 2010 at 9:25 pm
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 May 5, 2012 at 3:07 pm
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.