Answer:
$3712.
Step-by-step explanation:
We have been given that Aileen deposited money into an account compounded semiannually at a rate of 2.1%.
To find the principal amount we will use compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,
A= Amount after T years,
P =Principal amount,
r = Interest rate in decimal form,
n = Number of times interest is compounded per year,
T = Time in years.
Let us convert our given interest rate in decimal form.
[tex]2.1\%=\frac{2.1}{100}=0.021[/tex]
Upon substituting our given values in above formula we will get,
[tex]3952.08=P(1+\frac{0.021}{2})^{2*3}[/tex]
[tex]3952.08=P(1+0.0105)^{6}[/tex]
[tex]3952.08=P(1.0105)^{6}[/tex]
[tex]3952.08=P*1.0646770855930465[/tex]
Let us divide both sides of our equation by 1.0646770855930465.
[tex]\frac{3952.08}{1.0646770855930465}=\frac{P*1.0646770855930465}{1.0646770855930465}[/tex]
[tex]3711.9987397856=P[/tex]
[tex]P\approx 3712[/tex]
Therefore, Aileen deposited approximately $3712 in her account.
