Answer :
In order to determine the money you have to invest now to obtain $100,000 after 18 years, use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where,
P: principal = ?
A: amount after t years = 100,000
r: APR in decimal form = 0.11 (11%)
n: times of the compounded interest at year = 4 (quarterly)
t: time = 18 (years)
Solve the equation above for P, replace the values of the other parameters and simplify:
[tex]\begin{gathered} 100000=P(1+\frac{0.11}{4})^{4*18} \\ 100000=P(1.0275)^{72} \\ P=\frac{100000}{(1.0275)^{72}} \\ P\approx14181.04 \end{gathered}[/tex]Hence, you need to invest approimately $14,181.04 to obtain $100,000 after 18 years.