Effective Interest Rate Calculator

This effective interest rate calculator finds the effective interest rate per period and the total rate of return by considering a nominal interest percent & the no. of compounding intervals per period. Below the tool you can find the formula used.


Nominal interest rate per period (r):*
Compouding freq. per period (n):*
Number of periods (t):*

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What is the formula for the effective interest rate?

No matter if you are analyzing an offer for a loan or for a savings/deposit account, comparing those offers or plans by a comparable interest rate can help you decide correctly which offer best suits your needs. To do so you have to convert a nominal interest rate with a given compounding frequency into one with new compounding rules, either by applying the formula explained below or by using this effective interest rate calculator:

Effective interest rate:

Effective Interest Rate Formula

Total rate of return for a given number of periods:

Total Effective Rate of Return Formula

Where:

“i” is the effective interest rate that results for the new compounding interval per period.

 “r” is the nominal interest rate per period given initially.

“n” is the new compounding interval per period.

“t” is the number of periods.

Financial terminology related to compound interest

  • Nominal interest rate refers to the stated percentage rate you will find in bank offers.
  • Period which in most cases is a year, but it can be any interval as negotiated with the financial institution. For instance it can be a month, a quarter or a half of year.
  • Compounding times per period which indicates how often the interest gets capitalized to the principal within a period. Please take account of the fact that the compounding frequency per period should refer to the same period as the nominal rate per period. For instance if the interest given is yearly, the compounding intervals should state the number of times the interest is compounded within a year.
  • Number of periods is the total number of periods (years | months | any other time periods considered) taken into account within the calculation.
  • Effective interest rate is the effective percentage of interest that results after compounding.
  • Compounded interest rate is the total interest percentage earned for the given number of periods.

Example of an effective interest rate calculation

Let’s assume we have a savings account with a nominal rate of 5% compounded monthly and want to figure out which is the effective annual interest rate we will get and which is the overall rate of return we will get in a 10 years time.

Steps:

1. Find the effective annual interest rate: i = ( 1 + ( r / n ) )n - 1

i = ( 1 + ( 0.05 / 12 ) )12 - 1 = 0. 0.051161898  = 5.116189%

2. Estimate the total rate of return for 10 years: it = (1 + i)t - 1

it = (1 + 0.051161898)10 - 1 =  0.64700950 = 64.70095%.

19 Apr, 2015