Question

Aileen deposited money into an account in which interest is compounded semiannually at a rate of 2.1% how much did she deposit if the total amount in her account after 3 years was 3952.08?

Answer 1

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.

$A=P(1+\frac{r}{n})^{nT}$, 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.

$2.1\%=\frac{2.1}{100}=0.021$

Upon substituting our given values in above formula we will get,

$3952.08=P(1+\frac{0.021}{2})^{2*3}$

$3952.08=P(1+0.0105)^{6}$

$3952.08=P(1.0105)^{6}$

$3952.08=P*1.0646770855930465$

Let us divide both sides of our equation by 1.0646770855930465.

$\frac{3952.08}{1.0646770855930465}=\frac{P*1.0646770855930465}{1.0646770855930465}$

$3711.9987397856=P$

$P\approx 3712$

Therefore, Aileen deposited approximately $3712 in her account.

Answer 2

Answer:

3714

Step-by-step explanation: