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

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for future value $A$ 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. Here, $P$ is the initial deposit, $r = 0.09$ (since $9%=0.09$), $n = 12$ (compounded monthly), and $t = 6$. First, we are asked to identify $P$.

Step2: Determine the value of $P$

The problem states that $$550$ are deposited. So, $P = 550$.

Step3: Calculate the future value $A$

Substitute the values into the formula: [ \begin{align*} A&=550\left(1 +\frac{0.09}{12}\right)^{12\times6}\ &=550\left(1+ 0.0075\right)^{72}\ &=550\times(1.0075)^{72} \end{align*} ] Using a calculator, $(1.0075)^{72}\approx1.71147$. Then $A = 550\times1.71147\approx941.31$.

Answer:

$P = 550$, and the balance after 6 years is approximately $$941.31$