Questions: The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate. This is called the annual (or effective) yield and denoted as Y. Find the annual yield as a percentage, given the annual interest rate and the compounding frequency. Y=(1+r/n)^n-1 Annual interest rate of 1.3%, compounded quarterly The effective annual yield is %. (Type an integer or a decimal rounded to the nearest thousandth as needed.)

Solution Steps

The annual interest rate \( r \) is 1.3%, and the compounding frequency \( n \) is quarterly, which means \( n = 4 \).

Convert the annual interest rate from a percentage to a decimal by dividing by 100: \[ r = \frac{1.3}{100} = 0.013 \]

Substitute \( r = 0.013 \) and \( n = 4 \) into the formula for the annual yield: \[ Y = \left(1 + \frac{0.013}{4}\right)^4 - 1 \]

Calculate \( \frac{0.013}{4} \): \[ \frac{0.013}{4} = 0.00325 \] Then add 1: \[ 1 + 0.00325 = 1.00325 \]

Raise \( 1.00325 \) to the power of 4: \[ 1.00325^4 \approx 1.0131 \]

Subtract 1 from the result: \[ 1.0131 - 1 = 0.0131 \]

Multiply by 100 to convert the decimal to a percentage: \[ 0.0131 \times 100 = 1.31\% \]

The effective annual yield is \( 1.31\% \).

Final Answer