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The annual interest rater, when compounded more than once a year, results in a slightly higher yearly interest rate. This is called the annual for effective) yield and denoted as Y. Find the annual yield as a percentage, given the annual interest rate and the compounding frequency Annual interest rate of 4.1%, compounded quarterly The effective annual yield is % (Type an integer or a decimal rounded to the nearest thousandth as needed.)

Respuesta :

Answer:

The effective annual yield is 4.163%.

Step-by-step explanation:

Consider the provided information.

It is given that annual interest rate of 4.1%, compounded quarterly.

We will use n = 4.

It is also given that r = 4.1%

4.1% can be written as:

[tex]\frac{4.1}{100}=0.041[/tex]

Now use the formula.

[tex]y=(1+\frac{r}{n})^n-1[/tex]

Now substitute the respective values in the above formula.

[tex]y=(1+\frac{0.041}{4})^4-1[/tex]

[tex]y=(1+0.01025)^4-1[/tex]

[tex]y=(1.01025)^4-1[/tex]

[tex]y=1.04163-1[/tex]

[tex]y=0.04163=4.163\%[/tex]

Hence, the effective annual yield is 4.163%.

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