In order to determine how much is the amount the woman should invest, use the following formula for the amount of money earnt with compound interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where,
A: amount obtained after t years = $45,000
P: principal investment = ?
r: percentage rate = 6% = 0.036
n: times at year = 2 (semiannually)
t: time = 15 years
Replace the previous values of the parameters and then solve for P, as follow:
[tex]\begin{gathered} 45,000=P(1+\frac{0.06}{2})^{2\cdot15} \\ 45,000=P(2.43) \\ P=\frac{45,000}{2.43}=18,539.40 \end{gathered}[/tex]Hence, the woman should invest approximately $18,539.40
