karen opened a savings account and deposited $700.00 as principal. the account earns 9% interest, compounded…

karen opened a savings account and deposited $700.00 as principal. the account earns 9% interest, compounded annually. what is the balance after 2 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

karen opened a savings account and deposited $700.00 as principal. the account earns 9% interest, compounded annually. what is the balance after 2 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the values

$P = 700$, $r=0.09$ (since 9% = 0.09), $n = 1$ (compounded annually), $t = 2$

Step2: Substitute into the formula

$A=700\left(1+\frac{0.09}{1}\right)^{1\times2}=700\times(1 + 0.09)^{2}$

Step3: Calculate the value inside the parentheses first

$(1 + 0.09)^{2}=1.09^{2}=1.1881$

Step4: Multiply by the principal

$A = 700\times1.1881=831.67$

Answer:

$831.67$