We are asked to find the annual percentage yield (APY) for two different investment scenarios. (a) An investment with a 7.1% interest rate compounded monthly. (b) An investment with a 6% interest rate compounded continuously. The final answers should be rounded to two decimal places.

1. Problem Description

We are asked to find the annual percentage yield (APY) for two different investment scenarios. (a) An investment with a 7.1% interest rate compounded monthly. (b) An investment with a 6% interest rate compounded continuously. The final answers should be rounded to two decimal places.

2. Solution Steps

(a) For an investment compounded monthly, the formula for the annual percentage yield (APY) is:

$APY = (1 + \frac{r}{n})^n - 1$

where $r$ is the nominal annual interest rate and $n$ is the number of times the interest is compounded per year. In this case, $r = 0.071$ and $n = 12$.

$APY = (1 + \frac{0.071}{12})^{12} - 1$

$APY = (1 + 0.0059166667)^{12} - 1$

$APY = (1.0059166667)^{12} - 1$

$APY = 1.073424 - 1$

$APY = 0.073424$

Converting this to a percentage and rounding to two decimal places, we get 7.34%.

(b) For an investment compounded continuously, the formula for the annual percentage yield (APY) is:

$APY = e^r - 1$

where $r$ is the nominal annual interest rate. In this case, $r = 0.06$.

$APY = e^{0.06} - 1$

$APY = 1.0618365 - 1$

$APY = 0.0618365$

Converting this to a percentage and rounding to two decimal places, we get 6.18%.

3. Final Answer

(a) 7.34 %

(b) 6.18 %