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Chapter 8: Problem 61

What is effective annual yield?

Short Answer

Expert verified
Effective annual yield (EAY) is the annual rate of return on an investment accounting for the effect of compounding. The formula for calculating it is \(EAY = (1 + i/n)^{nt} - 1\), where i is the nominal interest rate, n is the number of compounding periods per year, and t is the time the money is invested for in years.

Step by step solution

01

Define the Concept

Effective Annual Yield (EAY) is a measure of the annual rate of return on an investment that takes into account the effects of compounding. It is a more accurate measure of return than simple annual interest because it accounts for situations where interest is reinvested and earns further returns before the year is over.
02

Break down the formula

The formula to calculate the effective annual yield is \(EAY = (1 + i/n)^{nt}\) - 1, where i is the nominal interest rate, n is the number of compounding periods per year, and t is the time the money is invested for in years.
03

Explain the calculation

EAY essentially calculates how much more money \(i\) the investment will yield at the end of one year after all the compounding has been applied. For instance, if an investment compounds quarterly (n=4) at a nominal rate of 10% per year (i=0.10), EAY would be calculated as \((1 + 0.10/4)^{4*1}\) - 1, which gives an EAY of approximately 10.38%.

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