find the amount in the account for the given ...
find the amount in the account for the given principal, interest rate, time, and compounding period. p = $700, r = 4%, t = 9 years; compounded quarterly a = $ (type an integer or decimal rounded to the nearest cent as needed.)
Answer
# Explanation:
## Step1: Identify compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years.
## Step2: Convert the interest rate to decimal
Given $r = 4\%=0.04$.
## Step3: Determine the value of $n$
Since it is compounded quarterly, $n = 4$.
## Step4: Substitute values into the formula
We have $P = 700$, $r = 0.04$, $n = 4$, and $t = 9$. Substitute these values into the formula:
\[
\begin{align*}
A&=700\left(1 +\frac{0.04}{4}\right)^{4\times9}\\
&=700(1 + 0.01)^{36}\\
&=700\times(1.01)^{36}
\end{align*}
\]
## Step5: Calculate $(1.01)^{36}$
Using a calculator, $(1.01)^{36}\approx1.43076878$.
## Step6: Calculate the value of $A$
$A = 700\times1.43076878\approx1001.54$.
# Answer:
$1001.54$