Answer
See below
Work Step by Step
(a)
Calculation of future value of amount can be done by using formula:
\[A=P\times {{\left( 1+\frac{r}{n} \right)}^{nt}}\]
Where A denotes the Future value of the amount, P denotes the Principal amount, R denotes the rate of interest, t denotes the number of years and n denotes the number of times compounding is done in a year.
Compute the Future value by substituting the values in the formula as mentioned below:
\[\begin{align}
& A=P\times {{\left( 1+\frac{r}{n} \right)}^{nt}} \\
& =\$2,000\times{{\left(1+\frac{0.06}{4}\right)}^{4\times1}}\\&=\$2,000\times{{\left(1+0.015\right)}^{4}}\\&=\$2,122.73\end{align}\]
Hence, the future value of the amount is \[\$2,122.73\]
(b)
Calculation of interest can be done with the mentioned formula:
\[r=\frac{A-P}{Pt}\]
Where A denotes the Future value of the amount, P denotes the Principal amount, r denotes the rate of interest, and t denotes the number of years.
Compute the interest rate by substituting the values in the formula as mentioned below:
\[\begin{align}
& r=\frac{A-P}{Pt} \\
& =\frac{\$2,122.73-\$2,000}{\$2,000\times1}\\&=\frac{\$122.73}{\$2,000}\\&=6.1percent\end{align}\]
Hence, the effective annual yield is 6.1%
