if $550 are deposited into an account with 9% interest rate, compounded monthly, what is the balance after 6…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Given $P = 550$, $r=0.09$ (since $9%=0.09$), $n = 12$ (compounded monthly), and we need to find $A$ when $t = 6$.

Step2: Substitute values into the formula

$A=550(1 +\frac{0.09}{12})^{12\times6}$ First, calculate the value inside the parentheses: $\frac{0.09}{12}=0.0075$, then $1+\frac{0.09}{12}=1 + 0.0075=1.0075$. Next, calculate the exponent: $12\times6 = 72$. So, $A = 550\times(1.0075)^{72}$.

Step3: Calculate $(1.0075)^{72}$

Using a calculator, $(1.0075)^{72}\approx1.71255$.

Step4: Calculate the final amount $A$

$A=550\times1.71255 = 941.9025\approx941.90$

Answer:

$941.90$