sebastian invested $1,800 in an account paying an interest rate of 4.3% compounded monthly. assuming no…

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

We have $P=$1800$, $r = 4.3%=0.043$, $n = 12$ (compounded monthly), and $t = 17$ years.

Step3: Substitute values into the formula

$A=1800(1 +\frac{0.043}{12})^{12\times17}$. First, calculate the value inside the parentheses: $\frac{0.043}{12}\approx0.0035833$. Then $1+\frac{0.043}{12}=1 + 0.0035833=1.0035833$. Next, calculate the exponent: $12\times17 = 204$. So, $A = 1800\times(1.0035833)^{204}$. Using a calculator, $(1.0035833)^{204}\approx2.077$. Then $A=1800\times2.077 = 3738.6$.

Step4: Round to the nearest hundred dollars

Rounding $3738.6$ to the nearest hundred dollars gives $3700$.

Answer:

$3700$