Given:
• Final amount, A = $80,000
,• Time, t = 10 years
,• Interest rate, r = 4.0% = 0.04
,• Number of times compounded, n = monthly = 12 times a year.
Let's find the amount she should invest to achieve her goal.
Here, we are to find the principal, P.
Apply the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = $80,000
r = 0.04
n = 12
t = 10 years
Substitute values into the formula and solve for P:
We have:
[tex]\begin{gathered} 80000=P(1+\frac{0.04}{12})^{12*10} \\ \\ 80000=P(1.0033333)^{120} \\ \\ 80000=P(1.49083) \end{gathered}[/tex]Divide both sides by 1.49083:
[tex]\begin{gathered} \frac{80000}{1.49083}=\frac{P(1.49083)}{1.49083} \\ \\ 53661.29=P \end{gathered}[/tex]Therefore, the amount she should invest is $53,661.29
ANSWER:
$53,661.29
