money is invested into an account earning 4.25% interest compounded annually. if the accumulated value after…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the accumulated value, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. We want to find $P$, and we know that $A=$25000$, $r = 0.0425$, and $t = 18$. Rearranging the formula for $P$ gives $P=\frac{A}{(1 + r)^t}$.

Step2: Substitute values into the formula

Substitute $A = 25000$, $r=0.0425$, and $t = 18$ into the formula $P=\frac{A}{(1 + r)^t}$. So $P=\frac{25000}{(1 + 0.0425)^{18}}$.

Step3: Calculate $(1 + 0.0425)^{18}$

$(1 + 0.0425)^{18}=1.0425^{18}$. Using a calculator, $1.0425^{18}\approx2.131$.

Step4: Calculate $P$

$P=\frac{25000}{2.131}\approx11731.58$. This value is closest to $$11820$.

Answer:

B. $$11,820$