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

3714

Explanation:

Answer 2

$3712.

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+(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\%=(2.1)/(100)=0.021`

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

`3952.08=P(1+(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.

`(3952.08)/(1.0646770855930465)=(P*1.0646770855930465)/(1.0646770855930465)`

`3711.9987397856=P`

`P\approx 3712`

Therefore, Aileen deposited approximately $3712 in her account.