Effective Annual Rate
The Effective Annual Interest Rate or Effective Annual Rate, is the rate of interest a depositor receives in a year time after accounting for the effects of compounding. This is the proportion at which an investment grows in worth when interest is credited more often than once a year. Annual Equivalent Rate and expressed as a percentage in annual basis.
The main usage of Effective Annual Rate is for compare the annual interests among different compounding terms, which are as daily, monthly, annually, or extra. The main two aspects that make Effective annual ratediffer from the Annual percentage rate (APR) are as follows. (1) the effective interest rate normally does not incorporate one-time charges such as front-end fees. (2) The effective interest rate is normally not defined by legal or regulatory authorities (as APR is in many authorities). In the comparison, if we are taking two plans, the interest plan with the advanced effective annual rate would be measured the better plan among that. The Better earning plan would be the interest plan which has the higher effective annual rate.It gives an idea to the Depositor or Borrower what once a year paid rate would be the same to the interest being paid, it is used for the effects of differences in the occurrence and timing of interest expenditure. In other ways we can say, Effective Interest Rate is a tool and the control which is more useful to comparing loan programs with different interest rates, compounding rate of recurrence and other charges.
For the detailed steps of EAR findings, let’s assume the following objectives as the letters assigned respectively;
S Final value of investment
P Initial value of investment
EAR Effective annual rate
r Annual percentage rate (APR)
k Interest periods per year
After a term of one year the final value, S , of a compounded interest investment with an initial value P compounded k times per year at an annual percentage rate of r is given by:
S = P (1 + r/k) k
After a term of one year the final value, S, of a simple interest investment with an initial value P at an annual percentage rate of EAR is given by:
S = P (1 + EAR)
Arranging these two equal of ‘s’, we will get:
P (1 + EAR) = P (1 + r/k) k; separating each side by P for a solving, we get:
(1 + EAR) = (1 + r/k) k ; again solving for EAR we get:
EAR = (1 + r/k) k – 1
Since APR is a factor in EAR
Effective Annual Rate calculation methods are dissimilar in different countries. For example in US the method is differ from Europe and Canada.
APR in the United States: APR is calculated by multiplying the number of periods by the cyclic interest rate. Therefore, if the monthly rate is 1%, the equivalent APR is simply 12%.
APR in Europe: APR is planned by compounding the monthly interest rate over the year, sometimes this rate is called the Annual Percentage Yield in the U.S. or Effective Annual Rate in Europe.
APR in Canada: The condition is a little more complicated, a compounding frequency of 2 per year is used, even though there may be 12 payments per year.
The consumers, who look for safe investments that grow from compounding of interest payments, should be concerned with the effective annual interest rate as it is a better indicator of the actual return on investment. Increasing the number of periodic payments increases the EAR; hence it is important for the investors, for seeking secure and short-term savings products.
Example for a solution
Assume 8.0% annual percentage rate, calculated monthly then EAR for this would
EAR = (1 + r/k)k - 1
EAR = (1 + 0.08/12)12 - 1
EAR = (1.006666666)12 - 1
EAR = (1.082999498) - 1
EAR = 0.082999498
EAR = 8.2999%.
Practical Scenario of MBR.
Generally, the Effective interest rate is directly proportional to compounding frequency. If the compounding frequency is higher than the AER will be higher.The customers, who look for secure savings that grow from compounding of interest payments, should be concerned with the effective annual interest rate as it is a good sign of the actual return on investment.
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