money is invested into an account earning 4.25% interest compounded annually. if the accumulated value after…
money is invested into an account earning 4.25% interest compounded annually. if the accumulated value after 18 years will be $25,000, approximately how much money is presently in the account?\na. $5,875\nb. $11,820\nc. $19,125\nd. $23,960\nplease select the best answer from the choices provided\no a\no b\no c\no d
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the accumulated amount, $P$ is the principal amount (initial amount), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. We want to find $P$, so we can rewrite the formula as $P=\frac{A}{(1 + r)^t}$.
Step2: Convert the interest rate to decimal
The annual interest rate $r = 4.25%=0.0425$, $A = 25000$, and $t = 18$.
Step3: Substitute values into the formula
$P=\frac{25000}{(1 + 0.0425)^{18}}$. First, calculate $(1 + 0.0425)^{18}$. Using a calculator, $(1 + 0.0425)^{18}\approx2.1045$. Then, $P=\frac{25000}{2.1045}\approx11870\approx11820$ (due to rounding differences in the calculation process).
Answer:
B. $11,820$