find the annual percentage yield for an investment at\na) 10.8% compounded continuously. %. (round to 3…

Explanation:

Step1: Recall the formula for APY with continuous compounding

The formula for the annual - percentage yield (APY) when compounded continuously is $APY = e^{r}-1$, where $r$ is the annual interest rate (in decimal form). For part (a), $r = 0.108$. $APY=e^{0.108}-1$

Step2: Calculate the value

Using a calculator, $e^{0.108}\approx1.11402$. Then $APY = 1.11402 - 1=0.11402$.

Step3: Recall the formula for APY with non - continuous compounding

The formula for the annual - percentage yield (APY) when compounded $n$ times a year is $APY=(1 +\frac{r}{n})^{n}-1$, where $r$ is the annual interest rate (in decimal form) and $n$ is the number of compounding periods per year. For part (b), $r = 0.119$ and $n = 2$ (semi - annual compounding). $APY=(1+\frac{0.119}{2})^{2}-1$

Step4: Calculate the value

First, $\frac{0.119}{2}=0.0595$. Then $1+\frac{0.119}{2}=1.0595$. Squaring it, $(1.0595)^{2}=1.12244025$. So $APY = 1.12244025-1 = 0.12244025$.

Answer:

a) $11.402$ b) $12.244$