Question

what is the correct way to annualize an interest rate in financial decisions?

Answer 1

Suppose a bank offer 12% interest rate and interest rate is compounded monthly,

In this case we need to annualize interest rate, the effective interest rate will be higher than the annual rate of interest.

Here is how to calculate effective rate of interest

The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, the effective rate or the annual equivalent rate

So if nominal interest rate (i), number of compounding in a year is (m), effective interest will be

Effective interest rate = (1 + i/m) ^m -1

Where,

Nominal interest rate (i) = 12% per year

Number of compounding in a year (m) = 12

Let's put all the values in the formula

Effective interest rate = (1 + 0.12/12) ^12 - 1

                                              = (1 + 0.01) ^12 - 1

                                              = (1.01) ^12 - 1

                                              = 1.12683 - 1

                                              = 0.1268

So annual effective interest rate is 12.68% per year

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