Question

How much should a mother invest at the time her daughter is born in order to provide her with $100,000 at age 18? Assume that the interest is 3% compounded semiannually

Answer 1

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,

$\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ \\ 100000=P\cdot(1+\frac{0.03}{2})^{2\cdot18} \\ \\ 100000=P\cdot(1+0.015)^{36} \\ \\ 100000=P\cdot1.709 \\ \\ P=\frac{100000}{1.709}=58508.97 \end{gathered}$

So, the mother should invest $58,508.97