Answer
See below
Work Step by Step
(a)
Calculation of value of the annuity can be done by using formula:
\[A=\frac{P\left[ {{\left( 1+r \right)}^{t}}-1 \right]}{r}\]
Where A denotes the value of the annuity, P denotes the periodic deposit, r denotes the rate of interest, and t denotes the number of years.
Compute the value of the annuity by substituting the values in the formula as mentioned below:
\[\begin{align}
& A=\frac{P\left[ {{\left( 1+r \right)}^{t}}-1 \right]}{r} \\
& =\frac{\$520\left[{{\left(1+0.06\right)}^{20}}-1\right]}{0.06}\end{align}\]
Solve and simplify the equation as follows:
\[\begin{align}
& A\approx \frac{\$520\left[\left(3.207135472\right)-1\right]}{0.06}\\&=\frac{\$520\left(2.207135472\right)}{0.06}\\&=\frac{\$1147.71}{0.06}\\&=\$19,129\end{align}\]
Hence, the amount of annuity at the end of 20 years is\[\$19,129\].
(b)
Computation of the interest amount can be done by deducting the total of periodic deposit amount from the annuity value. Compute the interest amount as mentioned below:
\[\begin{align}
& \text{Amount of interest}=\text{Amount of annuity after 20 years}-\text{Amount deposited in 20 years} \\
& =\$19,129-\left(20\times\$520\right)\\&=\$19,129-\$10,400\\&=\$8,729\end{align}\]
Hence, the amount of interest at the end of 20 years is \[\$8,729\]
