Question

Plot by hand effective interest rate versus nominal interest rate for continuous compounding.

Answer 1

The interest rate shall take two forms: the nominal interest rate and the actual interest rate. The nominal interest rate does not take the compounding period into account. The effective interest rate takes into account the compounding cycle and is thus a more precise indicator of interest charges. A sentence that the "interest rate is 10%" means that interest is 10% every year, compounded quarterly. In this scenario, the average annual interest rate is 10% and the actual annual interest rate is 10%. Nevertheless, if compounding is more regular than once a year, the effective interest rate would be more than 10%. The more frequently the compounding happens, the higher the effective interest rate. The relationship between the nominal annual interest rate and the actual annual interest rate is as follows:

i_a = [ 1 + (r / m) ] ^m - 1
If "ia" is the effective annual interest rate, "r" is the nominal annual interest rate, and "m" is the number of compounding periods per year. A Nominal Interest Rate, r, is an interest rate which does not involve any consideration of compounding. Nominal means, "just in name," not the actual rate in this case.

The nominal interest rate is also known as the interest rate indicated. This value is based on basic interest and does not take into account the length of the compounding. The average interest rate is that of the compounding periods during the payment contract. This is used to compare annual interest rates between loans with different compounding periods, such as week, month, year, etc. Typically reported or nominal interest rate is lower than It's the successful one. And the picture below shows the real picture of the financial payments. The nominal interest rate is the annual interest rate times the number of cycles per year. It's year. For example, a nominal annual interest rate of 12% based on monthly compounding Means 1% interest rate per month (compounded). The nominal interest rate for compounding periods of less than one year is often greater than the comparable rate for compounding periods. Annual compounding (immediately after basic algebraic manipulations) Of the compound interest formula). Remember that the nominal rate is not multiplied Frequency is not clearly defined: the effective interest rate can not be used for any interest rate. Specified without knowing the frequency of the compounding and the rate. While there are some Conventions are used where the level of compounding is known by consumers The value of understanding the effective rate may not be known in particular. Nominal interest rates are not equivalent because their compounding intervals are the same. Same; efficient interest rates are right for this by translating nominal rates into annual interest rates Compound interest rate. For certain cases, subject to local laws, interest rates are the same as Cited borrowers and ads are focused on nominal, non-effective interest rates and could therefore understate the interest rate as opposed to the equivalent effective annual rate. The word should not be confused with simple interest (as opposed to compound interest) that is not compounded. The effective interest rate is often measured as if it were compounded annually. Effectiveness
The rate shall be measured as follows, i.e. where the rate is efficient and the rate is nominal. (as decimal, i.e. 12 percent = 0.12) and "m" the number of compounding periods each year. (e.g. 12 for monthly compounding):

i_a = [ 1 + (r / m) ] ^m - 1