ximena invested $340 in an account paying an interest rate of 1.5% compounded monthly. assuming no deposits…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula 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. Given $P = 340$, $r=0.015$ (since $1.5%=0.015$), $n = 12$ (compounded monthly), and $t = 20$.

Step2: Substitute values into the formula

$A=340(1 +\frac{0.015}{12})^{12\times20}$. First, calculate the value inside the parentheses: $\frac{0.015}{12}=0.00125$, then $1+\frac{0.015}{12}=1 + 0.00125=1.00125$. Next, calculate the exponent: $12\times20 = 240$. So, $A = 340\times(1.00125)^{240}$.

Step3: Calculate $(1.00125)^{240}$

Using a calculator, $(1.00125)^{240}\approx1.34935$.

Step4: Calculate $A$

$A=340\times1.34935 = 458.779$.

Step5: Round to the nearest hundred dollars

Rounding $458.779$ to the nearest hundred dollars gives $500$.

Answer:

$500$