jake opened a savings account and deposited $700.00 as principal. the account earns 7% interest, compounded…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert given values to appropriate form

The principal $P=$700$, the annual interest rate $r = 7%=0.07$, the number of times compounded per year $n = 4$ (compounded quarterly), and the time $t = 4$ years.

Step3: Substitute values into the formula

$A=700(1 +\frac{0.07}{4})^{4\times4}$. First, calculate the value inside the parentheses: $\frac{0.07}{4}=0.0175$, then $1+\frac{0.07}{4}=1 + 0.0175=1.0175$. Next, calculate the exponent: $4\times4 = 16$. So, $A = 700\times(1.0175)^{16}$.

Step4: Calculate $(1.0175)^{16}$

Using a calculator, $(1.0175)^{16}\approx1.32129$.

Step5: Calculate the final amount $A$

$A=700\times1.32129 = 924.903$. Rounding to the nearest cent, $A\approx$924.90$.

Answer:

$924.90$