find the amount in the account for the given ...

# Explanation: ## Step1: Identify the 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 the interest rate to decimal form Given $r = 3.5\%=0.035$. ## Step3: Determine the value of $n$ Since it is compounded monthly, $n = 12$. ## Step4: Substitute the values into the formula We have $P = 3630$, $r=0.035$, $n = 12$, and $t = 23$. $A=3630(1 +\frac{0.035}{12})^{12\times23}$ First, calculate the value inside the parentheses: $\frac{0.035}{12}\approx0.002917$, then $1+\frac{0.035}{12}=1 + 0.002917=1.002917$. Next, calculate the exponent: $12\times23 = 276$. So, $A = 3630\times(1.002917)^{276}$. $(1.002917)^{276}\approx2.2577$. Then $A=3630\times2.2577\approx8195.45$. # Answer: $\$8195.45$