Answer
$a.\quad {{\$}} 63,449.32$
$b.\quad {{\$}} 44,267.09$
Work Step by Step
The amount A after t years due to a principal P
invested at an annual interest rate r, expressed as a decimal,
compounded n times per year is $A=P\displaystyle \cdot\left(1+\frac{r}{n}\right)^{nt}$
If compounding is continuous, $A=Pe^{rt}$
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$a.$
The cost A, after t=20 years, with P=30,094, r=0.038, compounded annually (n=1), is
$A=30,009(1.038\approx{{\$}} 63,449.32$
$b.$
The present value $P$ of $A$ dollars to be received after $t$ years,
assuming a per annum interest rate $r$ compounded continuously, is $P=Ae^{-rt}$
$t= 2033-2015=18$
$P=63,449.32e^{-0.02\cdot 18}\approx{{\$}} 44,267.09$
