Calculating the actual Effective Annual Return

Learn to Calculate Actual Effective Annual Rate

All of us want to be smart and successful in our personal finance matters. Part of this endeavour is about being aware of the time value of money. Below are some computation methods related to time value of money.Read and find out how to calculate the actual effective annual rate (EAR).

One problem that you may be aware of is that when you deposit money in a Fixed Deposit (FD) account, you will be asked about how long you want to keep your deposit. The options are usually 1 month, 3 months, 6 months, 1 year and longer. You will be left to decide the period you want based on the different interest rates that vary according to the tenure.
Theory

Scenario 1 - 12-month FD
Based on the above scenario, assume you are depositing RM10,000 in FD for a period of 12 months. At the end of the term, you will receive your principal amount of RM10k and 3.7% interest (RM370)

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

Scenario 2 - 6-month FD

Assuming you decide to keep the money for a 6 month tenure, you will get

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

When you renew the FD without withdrawing the interest earning, you will have RM10,170 in the FD for another 6 months. So, by the end of the year in question, you would have got 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%

You can use the following formula to calculate the EAR that you will get.

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. More often than not, these rates do not reflect the actual annual rate. Any interest rate is termed as nominal if the frequency of compounding (e.g. a month) is not the same as 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 frequently you compound, the higher the EAR you will get.

When comparing plans, it is imperative that you calculate the respective EAR for each plan. Use an EAR converter to compare the plans.