Questions: Determine the effective annual yield for 1 invested for 1 year at 3.9% compounded quarterly. The effective annual yield is %. (Round to the nearest hundredth.)

Solution Steps

To determine the effective annual yield for an investment compounded quarterly, we need to use the formula for compound interest. The formula for the effective annual yield (EAY) is given by:

\[ EAY = \left(1 + \frac{r}{n}\right)^n - 1 \]

where \( r \) is the annual interest rate (expressed as a decimal), and \( n \) is the number of compounding periods per year. In this case, \( r = 0.039 \) and \( n = 4 \).

Let the annual interest rate be \( r = 0.039 \) and the number of compounding periods per year be \( n = 4 \).

The formula for the effective annual yield (EAY) is given by:

\[ EAY = \left(1 + \frac{r}{n}\right)^n - 1 \]

Substituting the values of \( r \) and \( n \):

\[ EAY = \left(1 + \frac{0.039}{4}\right)^4 - 1 \]

Calculating the expression:

\[ EAY = \left(1 + 0.00975\right)^4 - 1 = (1.00975)^4 - 1 \approx 0.039574091474378514 \]

To express the effective annual yield as a percentage:

\[ EAY \text{ (percentage)} = EAY \times 100 \approx 3.9574091474378514 \]

Rounding to the nearest hundredth gives:

\[ EAY \text{ (percentage)} \approx 3.96 \]

Final Answer