# Calculating Effective Annual Rate ( EAR ) and Compounded Annual Growth Rate ( CAGR )

Accurate estimation of the return on investment is important to an investor. It not only gives him a clear picture of how his investments have fared, but also enables him to compare the returns of fundamentally different investment options available in the market.  The EAR and CAGR are two of the most important concepts/calculators, which cover the investments with a fixed rate of return and those which do not grow at a constant rate and fluctuate widely over the holding period.

Effective annual rate (EAR)

You might have noticed that interest rate tables for fixed deposits sometimes have an additional column called the effective rate or yield, in addition to the interest rate payable per annum, as seen in the table below.

 Non cumulative  Deposits Cumulative Deposit Period (months) Monthly % p.a Quarterly % p.a Half yearly % p.a Yearly %p.a Effective Yield % pa 12 8.65 8.71 8.81 9.00 9.00 24 9.11 9.18 9.28 9.50 9.95 36 9.34 9.41 9.52 9.75 10.73 48 9.34 9.41 9.52 9.75 11.27 60 9.34 9.41 9.52 9.75 11.85

The nominal interest rate payable per annum is not a true indicator of the returns earned – how many times this interest is paid, or the compounding frequency makes all the difference ! The more the number of times the interest is paid in a year, higher is the compounding effect, hence higher the effective rate.  For eg- I deposit an amount of Rs 1000/- in a bank at an interest rate of 10 % per annum.

If the interest is paid at the end of each year, my balance at the end of the year is 1100. Hence the effective annual rate is 10 %, same as nominal rate.

If the interest is paid semi annually, after every 6 months, the ending balance would be Rs. 1102.50, which means I am actually earning 10.25 % per year, which is the effective annual rate.

If in the same example, interest is paid quarterly, the ending balance after a year is Rs. 1103.81, making the effective annual yield 10.38 % per annum.

Compounded Annual Growth rate (CAGR)

Not all investments have a fixed rate of return or grow at a steady pace. The most common example are units of a mutual fund, especially equity based ones, whose values fluctuate widely during the term or holding period. So it is important to know the average returns per annum the investment has earned. The CAGR formula uses the principal value at the start, the ending value of the investments and the number of years or time periods of holding.

An investment of Rs 1000 which grows to Rs 1500 after 2 years – CAGR is 22.47 % p.a

An investment of Rs 1000 which grows to Rs 1500 after 3 years – CAGR is 14.47 % p.a

Hence CAGR evens out the effect of volatility, and expresses the growth as a constant return per annum to enable an easy comparison with alternative investment avenues.

The concept of CAGR is widely used in financial planning  – to determine at what rate the investment should grow in order to reach the target amount after a specified number of years.