Comparing Effective Annual Yields of Investments

Question:

Determine the effective annual yield for each investment. Then select the better investment. 2.93% compounded semiannually; 2.92% compounded monthly LOADING... Click the icon to view some finance formulas. Question content area bottom Part 1 Select the correct choice below and fill in the answer boxes within your choice. (Round to the nearest hundredth as needed.) A. The first investment, 2.93 % compounded semiannually, is the better investment because the effective annual yield for the first investment is enter your response here% and the effective annual yield for a 2.92 % compounded monthly investment is enter your response here%. B. The second investment, 2.92 % compounded monthly, is the better investment because the effective annual yield for the first investment is enter your response here% and the effective annual yield for a 2.92 % compounded monthly investment is enter your response here%. Click the icon to view some finance formulas.Click the icon to view some finance formulas.Click the icon to view some finance formulas.Click the icon to view some finance formulas.)Click the icon to view some finance formulas.Click the icon to view some finance formulas.Click the icon to view some finance formulas.Click the icon to view some finance formulas.)

Answer:

To determine the effective annual yield (EAY) for each investment, we can use the formula for effective annual yield:

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

where:

( r ) is the nominal interest rate (as a decimal),
( n ) is the number of compounding periods per year.

Investment 1: 2.93% Compounded Semiannually

( r = 0.0293 )
( n = 2 ) (since it is compounded semiannually)

[ EAY_1 = \left(1 + \frac{0.0293}{2}\right)^{2} - 1 ]

Calculating:

[ EAY_1 = \left(1 + 0.01465\right)^{2} - 1 ] [ EAY_1 = (1.01465)^{2} - 1 ] [ EAY_1 = 1.0295 - 1 ] [ EAY_1 = 0.0295 \text{ or } 2.95% ]

Investment 2: 2.92% Compounded Monthly

( r = 0.0292 )
( n = 12 ) (since it is compounded monthly)

[ EAY_2 = \left(1 + \frac{0.0292}{12}\right)^{12} - 1 ]

Calculating:

[ EAY_2 = \left(1 + 0.00243333\right)^{12} - 1 ] [ EAY_2 = (1.00243333)^{12} - 1 ] [ EAY_2 \approx 1.0294 - 1 ] [ EAY_2 \approx 0.0294 \text{ or } 2.94% ]

Summary of Results

Effective Annual Yield for 2.93% compounded semiannually: 2.95%
Effective Annual Yield for 2.92% compounded monthly: 2.94%

Conclusion

The better investment is the first investment (2.93% compounded semiannually) because it has a higher effective annual yield.

Final Answer