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 (initial amount), $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. We need to solve for $P$, so we can rewrite the formula as $P=\frac{A}{(1 + r)^t}$.

Step2: Convert the interest rate to a decimal

The annual interest rate $r = 4.25%=0.0425$, $A = 25000$, and $t = 18$.

Step3: Substitute the values into the formula

$P=\frac{25000}{(1 + 0.0425)^{18}}$. First, calculate $(1 + 0.0425)^{18}$. Using a calculator, $(1 + 0.0425)^{18}\approx2.115$. Then, $P=\frac{25000}{2.115}\approx11820$.

Answer:

b. $$11,820$