Let the initial amount should be invested = P
The interest = 3% = 0.03
compounded semiannually, n = 2
From born to age 18, it will be 18 years
so, t = 18
So,
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ \\ 100000=P\cdot(1+\frac{0.03}{2})^{2\cdot18} \\ \\ 100000=P\cdot(1+0.015)^{36} \\ \\ 100000=P\cdot1.709 \\ \\ P=\frac{100000}{1.709}=58508.97 \end{gathered}[/tex]
So, the mother should invest $58,508.97
