Questions: Determine the effective annual yield for 1 invested for 1 year at 5% 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 can 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 nominal interest rate (in decimal form),
• \( n \) is the number of compounding periods per year.

In this case, \( r = 0.05 \) (5%) and \( n = 4 \) (quarterly compounding).

1. Convert the annual nominal interest rate to a decimal.
2. Use the formula for the effective annual yield.
3. Calculate the result and convert it to a percentage.
4. Round the result to the nearest hundredth.

We are given the annual nominal interest rate \( r = 0.05 \) and the number of compounding periods per year \( n = 4 \).

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

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

Substituting the given values into the formula:

\[ EAY = \left(1 + \frac{0.05}{4}\right)^4 - 1 \]

Calculating the expression:

\[ EAY = \left(1 + 0.0125\right)^4 - 1 = (1.0125)^4 - 1 \approx 0.0509 \]

To express the effective annual yield as a percentage, we multiply by 100:

\[ EAY\% \approx 0.0509 \times 100 \approx 5.09 \]

Final Answer