find the amount in the account for the given principal, interest rate, time, and compounding period. p =…

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:

$1001.54$