sompound
Question 16, 10.3.29
Determine the effective annual yield for $\$ 1$ invested for 1 year at $5.1 \%$ compounded quarterly.

The effective annual yield is $\square \%$.
(Round to the nearest hundredth.)

Step 1 ：Define the variables: \(P = 1\), \(r = 0.051\), \(n = 4\), \(t = 1\).

Step 2 ：Calculate \(A\) using the formula \(A = P \times (1 + \frac{r}{n})^{n \times t}\).

Step 3 ：Substitute the values into the formula to get \(A = 1 \times (1 + \frac{0.051}{4})^{4 \times 1} = 1.0519836921140666\).

Step 4 ：Calculate the effective annual yield using the formula \((A - P) \times 100\).

Step 5 ：Substitute the values into the formula to get \((1.0519836921140666 - 1) \times 100 = 5.1983692114066615\).

Step 6 ：Round the effective annual yield to the nearest hundredth to get approximately 5.20%.

Step 7 ：Final Answer: The effective annual yield is \(\boxed{5.20 \%}\).