Question

A 4.2% bond pays interest semiannually. Its YTM is 5.4%. The Equivalent Annual Yield (EAY) on this bond is ____%. Refer to Lecture 35-36 notes as needed. Round your final answer to 2 decimal places (example: enter 12.34 for 12.34%), but do not round any intermediate work in the process.

Answer 1

EAY = 5.47%

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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) = 5.4% per year

Number of compounding in a year (m) = 2

Let's put all the values in the formula

Effective interest rate = (1 + 0.054/2) ^2 - 1

                                              = (1 + 0.027) ^2 - 1

                                              = (1.027) ^2 - 1

                                              = 1.05473 - 1

                                              = 0.0547

So annual effective interest rate is 5.47% per year

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