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 interest is compounded per year, and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 7%=0.07$.

Step3: Determine the value of $n$

Since it is compounded quarterly, $n = 4$.

Step4: Substitute the values into the formula

We have $P = 700$, $r = 0.07$, $n = 4$, and $t = 6$. Substitute these values into the formula: $A=700(1 +\frac{0.07}{4})^{4\times6}$.

Step5: Calculate the value inside the parentheses

$\frac{0.07}{4}=0.0175$, and $1+\frac{0.07}{4}=1 + 0.0175=1.0175$.

Step6: Calculate the exponent

$4\times6 = 24$.

Step7: Calculate $(1.0175)^{24}$

Using a calculator, $(1.0175)^{24}\approx1.51999$.

Step8: Calculate the final amount

$A = 700\times1.51999\approx1063.993\approx1063.99$.

Answer:

$1063.99$