Comparing Effective Annual Yields of Investments

Determine the effective annual yield for each investment. Then select the better investment. 5.06​% compounded monthly​; 5.07​% compounded annually 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 second​ investment, 5.07 % compounded annually​, 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 5.07 % compounded annually investment is    enter your response here​%. B. The first​ investment, 5.06 % 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 5.07 % compounded annually 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.)

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

1. For the investment compounded monthly: [ EAY = \left(1 + \frac{r}{n}\right)^{nt} - 1 ] where:

   • ( r ) is the nominal interest rate (as a decimal),
   • ( n ) is the number of compounding periods per year,
   • ( t ) is the number of years (for EAY, we can set ( t = 1 )).

2. For the investment compounded annually, the EAY is simply the nominal rate.

Investment 1: 5.06% compounded monthly

• ( r = 0.0506 )
• ( n = 12 )
• ( t = 1 )

Calculating the EAY: [ EAY = \left(1 + \frac{0.0506}{12}\right)^{12 \times 1} - 1 ] [ EAY = \left(1 + 0.00421667\right)^{12} - 1 ] [ EAY = (1.00421667)^{12} - 1 ] [ EAY \approx 1.0514 - 1 ] [ EAY \approx 0.0514 \text{ or } 5.14% ]

Investment 2: 5.07% compounded annually

• The EAY is simply the nominal rate: [ EAY = 5.07% ]

Summary of Effective Annual Yields

• Investment 1 (5.06% compounded monthly): 5.14%
• Investment 2 (5.07% compounded annually): 5.07%

Conclusion

The first investment, 5.06% compounded monthly, is the better investment because the effective annual yield for the first investment is 5.14% and the effective annual yield for the 5.07% compounded annually investment is 5.07%.

Final Answer

B. The first investment, 5.06% compounded monthly, is the better investment because the effective annual yield for the first investment is 5.14% and the effective annual yield for a 5.07% compounded annually investment is 5.07%.