joseph invested $330 in an account paying an interest rate of 3.2% compounded monthly. assuming no deposits…

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 given values to the appropriate form

We have $P=$330$, $r = 3.2%=0.032$, $n = 12$ (compounded monthly), and $t = 13$ years.

Step3: Substitute the values into the formula

$A=330(1 +\frac{0.032}{12})^{12\times13}$. First, calculate the value inside the parentheses: $\frac{0.032}{12}\approx0.00267$, then $1+\frac{0.032}{12}=1 + 0.00267=1.00267$. Next, calculate the exponent: $12\times13 = 156$. So, $A = 330\times(1.00267)^{156}$. Calculate $(1.00267)^{156}\approx1.517$. Then $A=330\times1.517 = 500.61$.

Step4: Round to the nearest hundred dollars

Rounding $500.61$ to the nearest hundred dollars gives $$500$.

Answer:

$500$