Answer
See below
Work Step by Step
(a)
Calculation of value of the annuity can be done by using formula:
\[A=\frac{P\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]}{\left( \frac{r}{n} \right)}\]
Where A denotes the value of the annuity, P denotes the periodic deposit, 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 value of the annuity by substituting the values in the formula as mentioned below:
\[\begin{align}
& A=\frac{P\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]}{\left( \frac{r}{n} \right)} \\
& =\frac{100\left[ {{\left( 1+\frac{0.055}{12} \right)}^{12\times 30}}-1 \right]}{\left( \frac{0.055}{12} \right)} \\
& =\frac{100\left[ {{\left( 1+0.004583 \right)}^{360}}-1 \right]}{\left( 0.004583 \right)} \\
& =\$91,361\end{align}\]
The value of IRA at the end of 30 years after retirement is \[\$91,361\]
(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:
\[\begin{align}
& \text{Amount of interest}=\text{Value of IRA after 30 years}-\text{Amount deposited in 30 years} \\
& =\$91,361-\left(12\times30\times\$100\right)\\&=\$91,361-\$36,000\\&=\$55,361\end{align}\]
The amount of interest at the end of 30 years is\[\$55,361\].
