determine the effective annual yield for each investment. then select the better investment. 2.92%…

Explanation:

Step1: Recall effective - annual - yield formula

The formula for the effective - annual - yield (EAR) is $EAR=(1 + \frac{r}{n})^{n}-1$, where $r$ is the annual interest rate and $n$ is the number of compounding periods per year.

Step2: Calculate EAR for 2.92% compounded semiannually

For the first investment, $r = 0.0292$ and $n = 2$. $EAR_1=(1+\frac{0.0292}{2})^{2}-1=(1 + 0.0146)^{2}-1=1.0146^{2}-1=1.02941316 - 1=0.02941316\approx 2.94%$

Step3: Calculate EAR for 2.91% compounded monthly

For the second investment, $r = 0.0291$ and $n = 12$. $EAR_2=(1+\frac{0.0291}{12})^{12}-1$. Let $x=\frac{0.0291}{12}=0.002425$. Then $(1 + x)^{12}=1 + 12x+\frac{12\times11}{2!}x^{2}+\cdots+x^{12}$. Using the formula $(1 + x)^{n}=\sum_{k = 0}^{n}\binom{n}{k}x^{k}$, or simply calculating $(1+0.002425)^{12}\approx1.029457 - 1=0.029457\approx 2.95%$

Step4: Compare the effective - annual - yields

Since $2.94%<2.95%$, the second investment is better.

Answer:

B. The second investment, 2.91% compounded monthly, is the better investment because the effective annual yield for the first investment is 2.94% and the effective annual yield for the second investment is 2.95%.